I don't think you can (or should really) get rid of the subjectivity side of it. Realistically there is just no way on earth you can define exactly how much force you can do something with before it becomes a foul so short of just saying it's a total non-contact sport there has to be subjectivity to the decisions.
Personally I'm not massively keen on the challenge idea. I get the plus points of it but I just don't really think that's how it should work, partly because of the subjectivity of it (imagine you get one challenge, use it on something like the West Ham handball where VAR says nah what are you on about it's fine and then have to just suck it up), partly because it shouldn't be up to teams to work out whether the officials have messed up it should be the officials who deal with it, and partly because it's a low scoring and relatively low incident sport, so you'll effectively just see people challenging goals for the sake of it because there's few enough of them to make it worth a try and it's not hugely likely something else will happen that would make it more worthwhile.
When I was talking about the backstop idea it's more as just a general hoovering up of absolute clangers. Someone else is watching the game and sees something the ref missed or sees a replay of something and realises it's worse/not as bad as the referee initially thought and just says sorry you're going to have to change that you've made a really bad decision. That way you're not looking at mm offsides or watching a challenge 25 times in slow motion, you're just clearing up genuinely bad decisions rather than changing decisions that nobody would ever have complained about before. You can't put the genie back in the bottle so they can't start doing it that way now, but to me that's how it should have been implemented from the start.