There are multiple independent people in this very thread who have done the work to look at prof bonuses, ability scores and monster stats and determined what you have to do in order to make it "attacker rolls".
It is simple. Replace a +7 dex save with a 14+7 = 21 dex defence.
Replace a +X stat save with a 14+X stat defence.
Use the spell attack modifier to attack that stat defence.
The first set of relatively uninteresting issues are stuff like bless, which instead of adding to your saves now subtracts from stat-attacks, and abilities like the barbarian dodge, which now imposes disadvantage on dex-targetting attacks instead of advantage on dex saves. But none of those are tricky.
The interesting issues is things like "do you now get disadvantage making spell attacks against stats when in melee range". In a faithful refactoring, the answer is no; but you might want to make it yes for symmetry reasons.
But the list of things you listed to be concerned about? No problem.
---
Myself, I this transformation is illuminating.
The average 'save' defence starts at 14, and goes up with stats. Someone with 18+ strength and proficiency has the equivalent of plate and shield AC at level 1, and increasingly enchanted armor at higher levels, against Str-targetting attacks.
