I finished recapping - it's surprising how many caps they crammed in there! I didn't have any 75 mfd caps on hand so just tacked in some 68 mfd. The correct caps should arrive shortly.
I used some mineral spirits and q-tips to clean up the corner and made sure it was completely dry before powering it up.
The cap that burned up was going from the AC line to ground. I replaced it with a proper safety cap.
I slowly powered it up and just got static on AM, but FM showed signs of life. I cleaned the volume control with deOxit and hooked up a proper dipole FM antenna. Finally, music came booming through
AM is still not working but that's probably because I don't have the internal loop antenna plus trimmer cap connected.