"unique" solutions for maximum keys up to n=9 not pressed
iow
ailo aios
acfior achior cfiory chiory
fhikloy fhikosy
acfhinpwy
"unique" solutions for minimum keys up to n=9 pressed
elrvxz
bdkpvxyz cefrtvxz cehrtvxz
bdkmptvxz beklmptwx beklmtvxz beklprwxy beklpvxyz dgjnquvxz dgkmrtvxz djnpquvxz
"unique" means excluding combinations which have better subsets (eg iow ⊂ iowsh)
The most number of increasing resources while balanced pressed space is 12 (out of 15), belonging to maximum presses:
fiosw hiosw iopsw
afiosw ahiosw fiopsw hiopsw
The best ≤11 presses can do is 9, which makes sense, as each key produces 1 or sometimes 2 resources.
There may be better solutions with 12-14 keys pressed, but they're exponentially larger and I didn't bother to spend the time.
The least number of increasing resources while balanced is 3, belonging to minimum presses:
bdkpvxyz
bdkpuvxyz beklprwxy
Maximum presses can only do 5 at least, from
cfiory chiory
acfimort achimort
This one did not search 10-16 presses.
Found by a script enumerating all combinations.