This usage of a quarterstaff is historically attested (in fact, it predates the middle grip we're more familiar with from media), and your houserules seem to be well thought out and balanced well enough. As you say, "All other martial 2HW with 1d8 damage have some special properties," so houseruling a "new" 2H 1d8 martial weapon isn't unbalanced.
There are other games that model quarterstaves being used in this way, and although they don't give it any extra extra "oomph" for leverage (the difference is apparently more a matter of style), giving it a single 1d8 of damage without extra benefits in exchange for its usual 1d6/1d6 is consistent with D&D's weapon-modelling idiom.
Don't forget that all weapons used two-handed get one and a half times the Strength modifier as a damage bonus instead of the usual ×1 Strength bonus. If you weren't accounting for that already it might make the damage potential of a 1d8 quarterstaff slightly more than you were intending, but your reasoning still holds: most other martial 2H weapons that deal 1d8 also carry some other special effect, so this isn't overpowered.
That said, since the motivation for this houserule was to ensure a feat remained useful, and since the rules already allow the 2H use that the feat applies to, you might decide to drop the houserule. It's not a bad house rule, but if that's the only reason you were considering it, it's not necessary.