If done with correct form, I can't see how inverted rows would place more of a strain on the back than BB rows. Your spine should be in a neutral position the whole time; if you let your torso sag that could put strain on your lower back, but this can be solved by not doing that

Is there some particular problem you have with your back that causes this concern?
Putting a plate on your stomach sounds uncomfortable and difficult to balance. A plate in a rucksack on your back works okay. Chains wrapped around the chest also work.
One will eventually run out of ways to weight down IRs though. If you reach that point you could try BB rows, but perhaps not if you have back problems.