Not sure what I can do about Weapons Speed (not sure if I'd want to), but for the spells, my homebrew/houserule is a blanket +1 round of casting per spell level over 3. So a 4th level spell takes 2 rounds (in 5e terms, 2 actions), 3 rounds @ 5th, and so on.
It REALLY helps maintain that "gotta keep the foes off the mage/the mage safe" even when at levels where the mage could take care of themselves.
That's another thing for the 1e feel: Spell disruption. It happens. It screws you up. You lose the spell, no effect (or if you're feeling VERY 1e, give 'em a roll on yon Sorcerer's Wild Magic table, for a particularly 'bad" disruption).
I can not stress enough the XP for gold and keeping/incorporating training at level up. That, to me is the biggest mechanic crutch of a 1e style experience. Perhaps only matched by/along with...
Differing XP tables. Everybody levels at a different rate. "Simple" classes: Fighters, Thieves, et al. level the fastest. "Rarer/more complex" classes: I'd put your Barbarians, your clerics, your rangers here, level slower. The most unusual/rare/specialized powers classes: your Mages, Paladins, [Psions if you use them], et al. level the slowest to keep their "more powerful than everybody else" in check.