TBH if you're not finding the performance with the 1090T acceptable, an 1100T wouldn't cut it either; the core count is the same, and there's only a ~3% difference in core/boost clocks. So take the game's official minimum hardware requirements with a huge grain of salt.
Are you absolutely sure you're not GPU-limited? Do you have enough RAM?
For AM3+ your upgrade options are limited, and may not provide a perceptible boost over the 1090T. The fastest AM3+ processors that don't require heroic cooling (or a motherboard with beefed up VRMs) are the FX-8350 and FX-8370, but the time to buy one of those if you wanted to do an "AM3+'s last stand" sort of thing was probably 2-3 years ago. New ones are getting scarce and prices have gone up. If you want to go this route, your best bet is probably to find a used one for cheap on eBay, and cross your fingers that all the pins are straight and that an overclocker hasn't beat the crap out of it.
Although an FX-8350/8370 has 2 more cores and significantly higher clocks than the 1090T, IPC of the FX series is mediocre, so you won't see as much of a performance boost as those numbers would imply. IMO it does not really make sense to gamble on whether it will get your performance into the "good enough" range when you could be putting that money towards a more modern platform.
Yes, I know it is painful to upgrade across platform generations since you need to replace all of your RAM. But AM3+ really is at the end of the road (and has been for a few years now). And I say this as someone who still runs an FX-8350 as my primary home desktop.