Removal of the cap seems unlikely and increasing the refinement cap has been proposed/shot down numerous times.

I'd like to see Doff missions for refining. Rare + duration 20 hours and such, but it would at least allow players to refine more dilitium.

There is a doff assignment to refine 1000 dilithium more and its available to Lifetime subscribers only, (has a long cooldown time though

Correction, it's availible to everyone who's subbed for 1000 days.

or if you pay real cash to refine, set a limit. like 5$ nets you 10k Dil refined, or put something in the Cryptic Store to be able to add an extra 8k per buy. meaning the first unlock is a permanent 16k a day for that character.

It takes two days to run.

I would guess that hardly anyone has subbed for 1000 days without buying a lifetime sub

You'd be surprised. It's not 1000 days, though, it's 'only' 800.

They will not put anything in the C store to increase your dilithium refining limit, it is basically the same as saying everyone can increase their refining limit for free.
Turn Dilithium to Zen, Use Zen to buy Dilithium cap increase, refine more dilithium, pour more dilithium into exchange for more Zen.

Say you had 5 characters refining 8k a day, on account that is 40k dilithium, turn that to Zen at current rate of 87Dilithium per Zen = 459 Zen per day per account.

If you got this dilithium cap raise for Zen like you are proposing across all 5 toons
16k x 5 = 80k dilithium = 919 Zen per day
Per week 6436 Zen - basically manage to buy everything on C store within a few weeks
Cryptic would then lose all sales in the Z store as noone would pay cash for anything again, as such cost cutting is made, redundencies, less content, fewer players and game dies

I'm simply not in a position to spend the money to subscribe and i think i'm not alone in this.
A doff refine for non subscribers would be mighty helpful.

if you spend $5 worth of zen to refine dilithium say 45000 current prices 87 dilithium to 1 zen you'd get 43500...why not just uh i donno buy it? then keep refining what you got? next few days...i'd say you'd need at least 200k unrefined for this to be of any real use....just thought i'd add this... if you have characters with extra refined dilithium use dilithium exchange put up for 25 dilithium 1 zen then cancel switch characters take dilithium out of mini dilithium exchange bank type thing other character now has dilithium that other one wasnt using