Finally I have located some data on the cannon carried by the whalers and other British ships captured by USS _Essex_ during its cruise in the Pacific during the War of 1812:

_Georgina_: Six 18-lb.
_Policy_: Ten 6-lb.
_Atlantic_: Six 18-lb. long-barrel [This ship became _Essex Junior_]
_Seringapatam_: Fourteen unknown-weight (poss. 9-lb.)

Unattributed to any specific catch: Ten 6-lb.; four 18-lb.

At least ten 6-lb. cannon were added to _Atlantic_'s six 18s when it was taken up as _Essex Junior_. This leaves ten 18-lb., fourteen 9-lb., and ten 6-lb.

While the 18s are heavier than the 12-lb. cannon _Essex_ was designed for, they aren't as heavy as the 32-lb. carronades it was left with when Porter took command. So it's possible for _Essex_ to have been rearmed from its prizes thus (L; Long-range; C: Carronade; [O]: Original armament; [P]: From prizes):

6x 12-lb.L [O]; 10x 18lb.L [P]; 16x 24.lbC [O]; 10x 32-lb.C [O].

(I doubt the 9-lb. would have been all that useful beyond lowering overall weight.)

This brings _Essex_ closer to the number of guns it was designed for (42, not 46) as well as the type (26x 12-lb.L main deck; 16x 24-lb.C spar deck), bringing it back to the weight and balance the designer intended. If so inclined, Porter could have swapped _Atlantic_'s long guns for carronades, giving:

6x 12-lb.L [O]; 16x 18lb.L [P]; 16x 24.lbC [O]; 4x 32-lb.C [O].

One wonders how such a loadout would have affected the outcome of the fight off Valparaiso. :)

I just ordered a book with more info; if it adds any useful data, I'll add to this.