The answer is simple, but y'all are not gonna like it.
1. Eliminate bonus actions. Things are either an action or it's part of another action, but it's not an action on its own.
2. Eliminate short rests and anything that recharges with them. Including HP/HD.
3. Make all species traits passive.
4. Remove about 50% of all class features, including but not limited to weapon mastery, cantrips, action surge, sneak attack, smite evil, reckless attack, Hunter's Mark, metamagic, etc. Every class feature should be a limited use action or a passive always on buff.
5. Kill summoning, animated dead, familiars, beast pets, and other peripheral characters that use their own actions. Wild shape has fixed options.
6. Rework monsters to fall under the same rules. No bonus actions, limited special attacks (with no random recharge) and very few spellcasting monsters.
7. Cut as many reactions as possible from the game, including legendary actions.
It would be fast since PCs would only have a small amount of possible actions: move + attack, use a limited resource, use a skill, help, or defend. It's going to be tactically boring, but the lightning fast speed should make up for that.