All the info you need is in my guide in my sig.
It's a bit long tho, so I can answer to your questions briefly...
Like it was mentioned, both staffmods and max number of sockets are based on ilvl
But here's more info :
Staffmods Tiers vs iLvl
01 ≤ iLvl ≤ 11: T1, T2 (base T1)
12 ≤ iLvl ≤ 18: T1, T2, T3 (base T2)
19 ≤ iLvl ≤ 24: T1, T2, T3, T4 (base T3)
25 ≤ iLvl ≤ 36: T2, T3, T4, T5 (base T4) (D2C: iLvl ≥ 25)
37 ≤ iLvl ≤ 99: T3, T4, T5, T6 (base T5) (D2X only)
Each base Tier is randomized by :
20% chance of +1
50% chance to stay unmodified
20% chance of -1
10% chance of -2
But no, the max number of sockets is not equivalent to the magic affix.
And this 3os magic affix is not even based on the ilvl in the first place... it's based on the alvl, which is a number that comes from the relation between the ilvl versus the qlvl of each item.
Not that it's relevent here, cuz again, I'm talking about the prefix 'artisan' for 3os.
For any white pelt, the maximum of 3os is unlocked at ilvl 26.
So no, you sadly can't achieve your goals since ilvl 26 sets the staffmods on a base of T4, and they can drop max 2 tiers.