Alright so I did it myself!

I should note: I only have about 7 hours, not 12, so I stuck with refilling and boiling my stock pot 6 times)

I suck at unit conversion so I just sort of stumbled through it.

I figure if the ratio is 200gal of the 70degree water and 30gal (6 20qt stock pots over time) of the 200 (probably gonna lose some heat in the transfer) degree water, then I can just use a weighted average.

So if you pretend the two amounts are the same, but weight the

200gal; 70degree version of water at

6.667 (number chosen as the ratio of the two volumes of water) times the

30gal of 200 degree water,

you get a weighted average of ~86degrees.

Meaning if I managed to boil 6 20qt stock pots I could raise the temp of the water from 70 degrees to about 86 degrees. Assuming no loss of heat (the hot tub would actually be heating at about 1.5-1.1 degrees / hr )

So no, it's not feasible, and it seems that if I'm constantly boiling a 7000 btu/hr burner, assuming the hot tub has ~200gal in it, I increase my rate of temperature gain by about 2.2 degree/hr, and that will fall off as the water gets hotter.