Hey JR!
I just finished my Magnatone 310 (hehe it looks like a 210, but discreetly has the "mellow-bright" on a pull pot of the 410". 
So, I've also played the real deal and mine came out just like it. 
I don't get a clicking noise.  I can confirm the depth of the wobble isn't super great and my speed adjust (used a log pot but thinking Lin will "feel" better) is pretty lame to start til about halfway. 
I got the "squeal of life" too and was surprised cause I thouuuught there was no (-) feedback. But I guess cause of the cathode cap and resistor going to the speaker +??? There is some type of feedback?  *calling all gurus*  
Anyway, 20mfd was typically AC ripple hummy and unacceptable, went to 40mfd. 
Also, on the actual amp did you use a .1 in the tone control even though the side to cathode scheme says .05?  The real deal had .1 there. 
Also also, did you keep the input scheme original?  I went to a more fender with a 1meg grid ref to not rely on the guit pot and cause I want to use kybds in a true hi lo on the lo. 
Anyway, I'll goof around today and make a video and post the guts cause my layout seemed to work 

.  
PS, it sure sounds vintage 
 
  
PPS, how were your voltages?  The 210 scheme on the second triode plate is like 78vDC which is weird and the 410 is like 160-ish??  Mine was 160-ish. 
This thing is just too ripe for modding and re biasing.  Neat tone control though.  There are several little circuit aspects I don't understand and need to find some president in the waaay back books etc. 
Take care!
Andy