Fwiw I don't think Ryanair carry-on baggage limits are particularly small. They're 55cmx40cmx20cm which is actually slight more in one dimension than most US airlines (though thinner in the third dimension).

I actually think 1h40m is fairly safe if your incoming EI flight is on time. It's pretty quick to get out in T2 with a US passport since there are rarely many non-EU passports. If you're carry-on-only for EI then you can be out in 10-20minutes from landing. And walking over to T1 doesn't take long.

The main problem is that there can be a big queue for FR check-in desks for stamping. If you're carry-on only for then if you're pushy you can go up to another FR desk that doesn't have a line and get them to stamp it though.

Just make sure you've checked in online in advance and get your boarding pass stamped.

The worst case is having to pay for another flight. You might consider booking the backup flight now since it might be pretty cheap insurance. But more likely than not you'll make the 1h40m connection.