The method of attachment might be suspect, but using the speaker out as a reverb input has been done by others. It's a "foldback reverb" system. Ya could also call it a feedback reverb, as too much of it will result in feedback.
Think about it this way: You need to add reverb in your amp, but can't swing adding a tube. You need/want a low-impedance source of signal to drive the pan. The speaker output is already low-impedance, and more than enough signal available (guess 3w output, 4 or 8 ohm speaker, you get 0.6-0.8vRMS of low-impedance signal).
Now think like a Gibson designer and/or marketing dude... You have a circuit here which has 1 less tube than a VibroChamp (cheaper to retube, maybe), but has the VC's tremolo and it has reverb! You "kill Fender" on all fronts, and put an expensive effect in the lowliest student amp. Yeah, it feeds back if you turn it up too much, "... but it's got reverb!!"
You could make the 47k isolation resistor coming from the tank output more like 470k to see if it helps with the feedback at high volume/reverb settings, but it will obviously weaken the reverb at lower settings. You could add series resistance from the speaker terminal into one (or both) of the alligator clip leads.
I think it was Budda amps (maybe a different early-2000 boutique builder) who made a 5F6A Bassman-type amp with foldback reverb. The difference was they might have derived the reverb from the speaker output, but gave the reverb its own power stage and speaker. So you got dry and reverb, but coming from different speakers, and no feedback issue.