Alternatively, I may decide to get away from ability score bonuses at all and simply give racial abilities (i.e. Dragonborn breath weapon) to each race.
I think this is really the best way to simulate strength differences for a couple of reasons:
1) D&D in 4E and 5E is very intentionally terrible at actually connecting size and damage capacity. A Mountain Dwarf is just as dangerous as a Goliath, despite one being 4ft and 150lbs and the other being 8ft and 340lbs. Similarly carrying capacity and so on.
Whereas with racial abilities, you can make a differentiation - a Goliath can lift/pull 4x what a Dwarf can. Just have a similar thing so Small races can only lift/carry/etc. half of what medium can.
If there are other places it matters but wouldn't overcomplicate or overbalance rules, you could extend it to cover those, but unless you're moving back to bonuses/penalties instead of Advantage/Disadvantage I think it's best to just ignore it in a lot of edge cases.
2) This opens the door to a lot more flexibility generally, if you go less off ability scores for things like this (which don't make a ton of sense, and indeed never have in any edition).
Add Warforged and either Tabaxi or Aaracroka.
This is a good call. Newer players seem very keen on Tabaxi so that seems like the way to go.
The people saying the Bard should become a half-caster are being pretty silly though imo. That would cause an absolute riot given the popularity of Bards with players under 30 and that the vast percentage of D&D players who are new with 5E (the majority of 5E players, I suspect) only know them as full casters. That's not a new PHB move, that's a serious edition-change
if you want the new edition to sell
less lol and you want younger players to complain about "grognards ruining D&D" a lot.