Disclaimer: It's 2:45 AM here, and I'm only on the computer because I'm too tired to sleep. So anything I say may be really really stupid.
My thoughts on researching Currency were as follows: we are able to build libraries now. Those won't be the world's fastest builds, but in our core and semi-core cities we should have them up within the time that our second tech ahead is researched. At that time, we'll need something else to build, and, well, options are limited. Plus, with three luxuries now (and surplus luxes to trade for other luxes in the future), markets will be valuable happiness tools. Even with just three luxes the market will provide an extra happy face. My thought was that the sooner we get to build those, the better. It's not like we will be in a situation where we can easily say "oh well, it's wealth or units, I guess I'll build three more archers"... with any luck, the only thing that archers will do is suck down unit support.
Ironically, of the four research choices, I'd have ranked Mapmaking my fourth choice.

Pros and cons of the other choices as I see them:
Construction--most expensive tech, which is bad--but this may also mean we get to it first while others research something cheaper. It also has the merit of making the Great Wall available, which is a useful fallback for the Hanging Gardens in the unlikely event that we wouldn't get that somehow. (Which I think is unlikely.) Makes Aqueducts available, not that we have a lot of towns that really need those.
Code of Laws: Has the merit of being cheap to research (9 turns). It's not something that the AI researches a great deal. Which means that, assuming we want one of them to research Republic for us, we may want to prod them along that path by dropping CoL in their lap.
Mapmaking: To my mind, the ROPs are the ONLY thing this has going for it right now. It does open up the Harbor as a build, but our one coastal town is not ready to build one yet anyway (and when it is we can use another building type as a prebuild for it). The Great Lighthouse is obviously a non-starter. And in my experience, this is a pretty popular AI research choice (more so than either Currency or Code of Laws), so if we are going to work a trade I'd rather let them get Mapmaking and trade for it, than get Mapmaking and try to trade it away.
All that said, if you really want the ROPs going, I'll play along. But I really think either Currency or Code of Laws would be better trade bait. In fact, I will bet you one virtual penny that we see an AI with Mapmaking before either one of those techs. But if you want to switch off Currency, I'd much rather see Code of Laws, only because it will go very quickly. (My crystal ball says we actually get it in 8 turns). That would give us a chance to re-assess the situation at that time.
Note that England researched up to Polytheism rather than go for Currency. I think depending exclusively on her to give it to us is taking a risk we don't need to.
On merging workers into Lyons: I really don't think it's necessary. The limiting factor will not be those Temple of Artemis builds. Take a look at your F7 screen right now. We can't see Bad-Tibira, but it's Sumeria's #6 city. York we can see--it's a size 2 city in the middle of the jungle. Either would finish the Temple of Artemis about the time we are launching.
Now, note all those Pyramids builds. Those are actually 400 shields to finish, more than our Hanging Gardens. Judging by your last spoiler, the Sumerians should be about 11 turns from the Pyramids, if they are the first to get there. London is also building the Pyramids, though my guess is they will be woefully behind based on terrain up there. It may be worth getting Philo into Sumeria's hands so that they can build the Mausoleum of Mausollos, IF it looks like a cascade is going to hit us.
All this is a fancy way of saying that they have prebuilds going for the Hanging Gardens, but Sumeria is the closest tech-wise--and they just got Poly about 6 turns ago, so even if they are researching Monarchy I think it's about 20 turns out. THAT is the limiting factor--how fast they can get to Monarchy. If they aren't researching it now, they won't get it. So I almost hope you see them get another tech during your turnset.
Lyons is getting 8 spt right now. In a couple of turns it will grow and will then be getting 10 spt (assuming a second shield isn't corrupted, though it may be). So that 23 turns is an illusion. If we added in one worker, that would take it to 11 spt (I'm pretty sure that a second shield will be corrupt at that point). My advice re: a worker add would be to wait until Lyons grows, and see if it is actually getting 10 spt after corruption. If it is, do not add a worker (that worker will only add one shield even if it works the forest, as the other would be corrupted). We'll have 161 shields to go after the next two turns, then 9 or 10 more done on the growth turn, so either 152 or 151. At 11 spt, that's 14 turns. At 10 spt, it's 16. I don't think two turns will make the difference. I do think we should keep a couple workers around there to road/mine the non-BGs and road the forests, and if as we are getting into the late game it looks like those extra few shields could matter, go for it then. But for now I don't think adding a worker is criticial. If the difference is 9 spt vs. 11, it's a three-turn difference, and I could maybe be persuaded. But I've been thinking we need more workers, not less, so I'm reluctant to merge this early.
On Avignon worker and connecting the road: I think it's OK to connect the road. Poitiers (our southern river town) can spew out a few warriors, as it really has nothing else to do right now (this is a looking far ahead city). Leave it unconnected (it won't grow to a size that cares about luxuries anyway) and everything else can connect. I'd still crank out workers in Avignon, or at least one more worker. That will be needed in that area to irrigate all those plains and mine all those sugars in that area. Avignon was really put there to grab the iron before the Inca could, not to become a powerhouse producer.
A couple of random thoughts:
On whipping something in Orleans--I don't see the need. The library in 13 is perfectly good if we want it, if we think we need settlers instead, build those, and wait on the library. It'll be a while before we can very effectively whip the library anyway. The more I look at it, honestly, the more I think more settlers from Orleans is a good idea. There is a nice patch of land about 8-10 tiles northwest of where we're about to found our next city near the Incas. We could very possibly be able to get to that in time (and fill in in between with whatever crap is there). If we can do that, we may yet be able to get all that incense in the north. Nobody else has made a run at it. Basically, draw a mental triangle from our warrior just north of Persia, due east to the black, and then up to that jungle/marsh peninsula. We can grab some of that and we really should. IF we do that, it is an absolute must to take two of our workers and pair them up to road due north as soon as humanly possible. The pair that is about to irrigate the last tile near Tours can do that then get roading (or just get roading, Tours is fine for a bit). This land might suck... or we could even put the Forbidden Palace up there. Dreaming? Maybe. But I think it's important to be aggressive in settling right now, and I think you do too.
Finally, a few micromanagement notes:
1. If you're feeling whippy, do it in Chartres after this turn. A temple there would be quite handy to possibly block Sumeria from getting much closer.
2. Also after this turn, switch Cherbourg (harbor town) from forest to wheat, at least for that turn. It's getting a Curragh in 2 regardless, may as well try to grow it a little faster.
3. I'm an idiot, click on the Lyons city square before hitting Enter, and gain an extra beaker per turn. I'd almost say the same about Amiens, but that one gets corrupted anyway (still should work roaded forest tile on general principles).
4. I think I'd switch Rouen from granary to something more cultural (your choice).
5. Besancon should work the forest, not the lake, in my opinion--temple comes faster that way by 6 turns, at the cost of only growing at 2 fpt instead of 3. More optionally, you could switch Rouen to the two unworked BGs (workers are on scene) and give Besancon that cow, so that it could work 2 cows and a forest. That would let it grow in 6, temple in 14, and it could work BGs after that as well. Unlike Avignon, Besancon CAN be quite a good town.