I started out testing with Agri first - it doesn't slow down the first cow. Honestly, I prefer giving up the 20% discount. There's no time to improve the rice until much later, as lots of other improvements take precedence. And we can just tech Agri in 2t when we do need it. Cutting out Agri also makes the Oracle sling more of a possibility. AH-Wheel-Wtg lets us build the library on a nice schedule.
Reasoning behind Wheel:
My worker actions right now are to improve the eastern cow first, then road the gold 1N - this finishes just as the second worker comes out, so it doesn't waste a turn getting to cow. Then roading the northern cow after pasture nets the extra health, improve the river gold first and use the two tiles of road to not lose a turn going back to other gold (as well as save a turn for the settler), then one worker goes to clear the fallout for the second city. I'm 1t late on that (settler sits). Not sure at all if this is optimal, but we can just play a short set and spend some time optimizing through test play still.
I need to test this further, but I think Agriculture -> AH -> Writing may be a stronger opening for a few reasons:
1. In general, I'm dubious of the value of researching the Wheel early unless it is needed to hook up a strategic resource (i.e. horses, copper, marble, etc). Spending two turns building a road to save one worker turn in movement later is not a good trade off, especially early in the game when every worker turn is vital. In addition, these two worker turns used to build a road segment could have been better used to get a pasture or a gold mine on line 2 turns sooner. Now, if we need the Wheel very early to hook up the cows and/or the rice to avoid unhealthiness, then researching the Wheel early on makes more sense. Keep in mind that we may not have to climb the gold hill to lay down a road for quite some time since one will be hooked up due to being on the river.
2. Don't under-estimate the value of the 20% bonus. Sure, we can research Agriculture in 2 turns later in the game. But we could also use those same 2 turns to research a different tech 2 turns sooner. If we think we'll have to self-research Agriculture eventually (i.e. we won't get it in trade), it is more efficient to research it before AH. 20% bonus at 10 base beakers for 10is turns = 20 "free" beakers = 3ish extra turns working a gold mine.
3. I thought that the CS sling was off the table due to the associated risk and since DoP and getting Alphabet from Gandhi were more important. Do we really want to put that back on the table and have it influence our decisions? I'm fine either way, but we can't continue keep all of our options open, right?
Now, if two workers can keep up with resource improvements and keep cleaning up the fallout fast enough to keep our health issues under control, then I don't see the need to research the Wheel so early.