In the first Mass Effect, I wouldn't do anything to the combat mechanics, as they didn't bother me at all: I was playing an RPG, not a shooter.
What I *would* do is fix the damned inventory. Not remove it, but fix it. I'd have everything in the inventory stacked and ordered as it ought to have been in the first place: rather than being a list of discrete items, group items of the same type and rank, and stack items of the same type but different ranks in a context sensitive fashion: when I'm in a shop, I want to sell off my crap, I want the crap to be the stuff easiest to get at, whereas when I'm doing a loadout, I want to be able to get at my best stuff most easily. Also, don't force me to omnigel stuff when I'm picking something up and my inventory is full: let me omnigel my crap.