It sounds like you have already made your decision, but I think the problem you are having is definitely in the small tank size. As you noted, specific gravity is difficult to maintain in a small tank and shrimp are hyper sensitive to swings in specific gravity.
The easiest way to overcome this is by using an auto top off (ATO) system. You simply have another container of water (a gallon jug would probably be fine for that size tank), a float switch, and a transfer pump to move water from the container to the tank.
The downside is cost. The ATO would run you about $50, the pump you can get for $16, and you can probably come up with a jug for next to nothing.
I have one on my 75 because my overflows are very sensitive to evaporation (well, the change in water level really) and I'm often gone for a few days each week. My wife manages the fluctuations in my 37 for me with a few jugs of RODI
water while I'm gone since that overflow maintain siphon even at low water levels.
I think in the long run you'll find it easier to set up a 30 gallon tank where things aren't magnified so much as in the 10 gallon. You can always use your 10 as a quarantine tank.