I am not certain which exact cranks you have. Based on fixed axle, I assume you are running outboard style bottom brackets. Regardless whether more conventional like square taper, ISIS, or possibly some forms of Shimano Ocatalink styles, I have seen where to minimize bearing drag, either by design the BB cup is secured by preapplied locking compound, or the installer could not reach proper torque without serious drag.
Not exactly certain what situation caused yours to loosen. Your own troubleshooting seems to have it sorted out. If you have an outboard style setup, there should be no issues getting both sides properly tight, and then setting end play via the non drive crank bolt.
FWIW, on a personal machine of ours, I upgraded the BB's. This was a model year 2000 Co-Motion. Co-Motion had threaded the bottom bracket shells, both frame and eccentric to the then current shallower depth for cartridge style BB's. Upon installing the replacement aftermarket BB's, the bearings would bind. Ultimately, I discovered the threads were longer on the replacement BB's and would pinch the bearings and bind it up. To resolve the problem I had to machine the first few threads off the BB on each side to eliminate the pinch.
All the best and enjoy your machine.
PK