I secured the speakers in place using small mounting squares and zip ties.
Next, I finished the coin door repaint and mounted that into the cabinet.
The plastic pieces from the coin door were in such rotten shape that I ordered new buttons, bezel and coin return flaps from Lizard Lick. It should look pretty good with those in place.
When I got the cabinet, it was missing two sets of bolts/brackets that help secure the coin door in place. One of the guys on the BYOAC forums pointed me to The Arcade Boneyard, where I ordered the replacement pieces.