I'm going to go out on a limb and suggest something that runs counter to the gist of this thread : make HQ potions stronger, longer, but a much longer recast than their NQ counterparts.

If a stat potion is 10%, lasts 15 seconds, and has a reuse of 180 seconds, it is only offering a 10% boost for 8% of the time, or a grand total of 0.8% increase. Its HQ counterpart should be more like 20% for 15 seconds, with a 300 second reuse. That would confer grand total of a 1% boost overall.

This would bring relevancy to the NQ, an element of strategery as to which is more important, a smaller boost more frequently, or a greater boost less frequently.

HP/MP potions, and poisons, could work in a similar fashion. HQ providing the bigger boost, but NQ being usable more frequently.