Why are HMs STILL a stumbling block for GF after all these years? Poké Rides were not the answer (because those mons you summon aren't YOUR companions), and the partner's Secret Technique system in LGPE isn't expansive enough.
My idea is simply to give Pokémon innate abilities (separate from the three abilities we have now) that correspond to HMs, just like Secret Techniques, but apply them to every Pokémon. Make these abilities subject to the same badge limitation as HMs, again, just like STs. Then, remove HMs entirely - even in their TM forms - and make the moves themselves obtainable at the Move Tutor.
Example:
>Swampert can currently learn Surf and Waterfall
>It could formerly learn Strength, Dive, Rock Smash, Whirlpool and Rock Climb
>Give it the innate ability to perform all of these tasks in the overworld (as needed as obstacles are added or removed)
>Don't allow it to use these abilities until the proper badge is obtained
>Add all of the corresponding moves to its Move Tutor movelist as lv1 moves
This solves the problem of needing to feel like your team has an impact in the world, providing a deeper sense of progression, while doing away with the burdens of HM moves. It would remove all possibility of soft-locking the game. The moves themselves would still be available, but also wouldn't take up TM slots, freeing them up for more interesting moves.