Excellent you got it going! Well done!
Yes balancing is going to be a bit fiddly. If its caravans that go through your terrain, that could be either very low or very high. I've had games with the AIs sending 10+ caravans into my civ. That would be 100 hammers per turn if every caravan ended its turn on my tiles. And that is before the modifier from sending caravans from the capital.
But since they come from distance we could assume each caravan will be spending about 2-4 turns going in and out of our territory (out of about 8-10+ turns to in the total caravan loop [i.e. from their city to Palmyra and back]).
This would give you about 20-40 hammers every 8-10 turns which equates to about 2.5-4 hammers per turn. However it is heavily dependent on city placement - In other words a potentially very powerful bonus.
I'm sure my numbers are a bit off but I think caravans move at about 3 tiles per turn don't they?
Edit:
You might have to be careful with the bonus from each caravan originating from the capital. If I'm not mistaken the capital is usually where people send their external caravans from - this could potentially cause some major balance issues, especially if you are lucky in drawing a lot of AI trade routes.
I'd possibly keep a backup idea in mind in case that second part of the UA does prove to be a bit too over the top. Production is arguably the most powerful value in Civ 5 and the faster you get through the build queue the sooner you win. If it's too much you can always trim the bonus from your capital trade routes and put in place the other idea you had which was to let Palmyra caravans treat deserts tiles as roads. Not trying to change your UA around but its not a bad idea to consider tweaking the UA a bit if the production bonuses are a bit over the top.
For what its worth I think the screenshot below shows the peak of my success with attracting trade routes. Granted I don't have a lot of land but I'd still be getting a tonne of free production from the UA. This was a pure trade route oriented strategy on Diety that was focused around a rush to Colossus (using Egypts UA) and East India Company and the Market.