All reasonable questions but I think possible to solve.
I think the 90 minutes will inevitably need to be reduced to 70 or 80 minutes if you had a stop clock. You’re right, people would moan about that.
There can be guidelines on what type of stoppage leads to stopping the clock. Throw ins, corners and goal kicks shouldn’t need to stop the clock but there should be a sensible 15-20 second time limit for taking them at which point the clock stops automatically (like an NBA shot clock). Free kicks the team can choose to take quick or elect to stop the clock, penalties the clock should stop, subs stop the clock.
All injuries lead to a stopped clock, feigned or not.
But this is just me making things up in my head on the fly. I think there needs to be a systematised manual with guidance like this that is very precise in its execution. It can be owned by official timekeepers who know exactly how to stop the clock, and they can be independently spot checked when needed for accuracy. This is pretty much how it works in Rugby.
I know fans would moan initially as they always do, but I would hope eventually they would see the benefit (less play acting, more predictable game length vs. current system as teams get used to the rules).