Maybe harnesses could allow you to carry one extra attack in hand from round to round. This is still a little bit of increased hand size, but you don't get unlimited stacking of armor.
My first thought was that this would be interesting if only for the negative synergy with Blind Rage. It's a fiddley enough idea that I'd be interested to test it, but my instinct is skepticism. That said, if you can't keep blocks or moves or boosts... I donno. I'd have to see how it shook out.
Giving the harnesses "you can keep one extra non-harness card at the end of the round" is enough to prevent infinite stacking. My first idea was to stick to armors, but it is true it can be any type(s) of card. It needs testing I suppose.