It sounds as if you might have tried the wrong capo. They vary, and some are much easier to use than others. No reason a capo should make a guitar sound strangld, just higher, which is what you'd be aiming to achieve by tuning higher anyway.

And any problem in working out what chord you are actually playing which you get with a capo would arise just the same if you retune higher. Tune one semitone higher, as you said, and your A shape would gve you Bflat, and your D shape woudl get you Eflat.

It'd be unlikely to hurt the guitar, but working out what chord you were playing might hurt your head.

And of course the sound would be just the same as if you stuck a capo on the first fret and didn't worry about retuning.