bad news: different form factor

better news: it's a smaller (thinner) form factor

A transplant of parts may work, but that looks like an "L" shaped PCB lies within . . . which could prove problematic . . .

. . . for adapting the adapter's connector to connect to the Pismo's different connector . . . :?:

. . . $14 sounds like a decent bet and some playtime since you've got that case in hand.