Another potential option I was running around my head is that armor reduces the size of the crit die. So D armor doesn't reduce at all, C armor reduces once, B armor reduces it twice, and A armor reduces it three times. Anything that's reduced below a D6 can't do crits at all against this armor.
That's a good idea - makes armour more useful but doesn't increase the book-keeping very much. Doesn't solve the car punching issue though, as civilian cars and trucks have D armour. It's more to remember, but vehicles bumping the armour crit die up 2 levels versus personal scale weapons would seem to work - means best crit die will be d8 vs a vehicle, and being armoured makes that less likely. A vehicle with A or B armour can't be critted at all by personal firearms or melee attacks then.
Going back to this idea, would it be simpler to allow the armour roll to 'anti-crit' so if you roll 2 successes the armour blocks 2 damage AND the crit from happening? If the crit attack was 3 successes, it'd still be a critical, but only one dice roll instead of two, and 3 successes on the armour roll could block that, and so on.
This would also emulate that body armour may save your life from a lethal injury but you still end up taking damage to Health from the concussive effect of the bullet, etc.
It wouldn't happen that often either, as getting 2 success on type D or C armour isn't that easy/likely.
This doesn't help with the issue of punching a car til it explodes, but Grimmshade's suggestion of a d6 crit die for blunt attacks against a vehicle would work for that. Another option would be to 'degrade' a personal weapon's crit dice 2 levels versus vehicle scale targets, unless the weapon is also vehicle scale.