Is there a continuous hole front to back through the tube you've arrowed?***
If the end had been flat, a nut and washer could have easily secured the bolt of a pushed-through binding post.
As things stand, your arrow is pointing to a perfectly angled and aligned solder 'bucket'.
Only one of the 4 is slightly less accessible. With a hot enough (non-precision) iron....
they were (almost literally) made for soldering the bared ends of pushed-through wires into place.
If you're concerned about the permanence, you could easily fit flying 4mm banana sockets on the wires say 3-4 inches from the back panel.
Unless you D.I.Y., the alternative of removing what's there and fitting 4mm posts / sockets looks like it might be pricey .....might steer you toward the solder option.
***Looking at your photo in post #4 there's no hole through - but a drill will make sure there is. May sound a bit drastic but, short of finding the correct size of plug, I can't see as you've got anything to lose by drilling / soldering - provided you ensure no metal shards / solder blobs are left floating within.
(Look where the metal strip from the socket passes under those 2 diodes....where the strip's lifted, it's not far off shorting to them as it is).
P.S. Don't fancy soldering? Get it to me, I'll gladly do it.....probably for around a quarter of what you get quoted for socket replacement 🤑
Do you know if the amp works by the way? 😏