You say that both Side Bands work - yes.
Problem is on "AM":
* No "AM" TX.
* No adjustment to L20, or L23 possible (both used for "AM" settings).
Since your problem is only with "AM" I would blame the (LSB, USB, AM) MODE switch circuit while in "AM" mode or related parts in that circuit.
* There should be "approximately 8V" (8V) constant (always) to the MODE switch, then to the "AM" terminal, then to "D85", and ends at "D95" feeding L20 and L23 adjustments.
* In Receive .... With the MODE switch on "AM" check for the 8V at both sides of diode "D95" and "D85". (NOTE that the "AM" 8v also goes to "Q24" transistor before going to "D85" and "D95".)
* If there is no voltage on one side of "D95"..... "D95" is bad or a short to board ground on that circuit side (going towards L20 or L23) . (Check for solder blobs causing shorts on Trace side of board.)
* If there is no voltage either side of "D95" ...... check both sides of diode "D85" for 8V.
* If "D85" shows no voltage on both sides then check for 8v at the "AM" terminal of the "MODE" switch while still in the AM" setting.
** If there is no 8V at the MODE switch terminal of the "AM" side then the MODE switch is bad.
**If there is 8V at the MODE switch terminal of the "AM" side then check for cut trace or wiring problem going to "D85" and "Q24".
* If, at one time, the MODE switch was set to "AM", and having 8V at that terminal (that also goes to "D85" and "Q24"), was ever shorted to ground it could have burned out that contact tips (inside the MODE switch) for the "AM" side.
* If the MODE switch is bad (no 8V for "AM") you may be able to use another set of contacts on the same "MODE" switch assembly, just make sure you connect to the right contact tips.
At this point I should stop here, but the following is important too:
You have turned VR7 and made changes to the radio adjustments.
(VR7 is for the LOCKED TX only adjustment .... The Clarifier is for the Receive only adjustment (if you turn the clarifier for any reason, you're still off the TX frequency).
* VR7's adjustment is set once during the alignment process .... Transmit (TX) only (not Receive).
* Once set VR7 is locked to that setting, VR7's adjustment must be exact and is the only adjustment for being on frequency during TX on SSB, other wise you would sound like Donald Duck during TX to the rest of the world.
*** This is the reason why the clarifier should be UNLOCKED letting the "Clarifier" control both Transmit and Receive at the same time (at all times) with VR7 no longer used and out of the circuit. (All previous adjustments need to be redone once the Clarifier is UNLOCKED to make sure that the Clarifier knob is centered at the 12o'clock position.)
You say that SSB works fine so this means that the "VR7" circuit should also be fine since it's common to all modes .... in case you want to check the circuit ........
If the clarifier is stock, VR7 should work to change TX MODE frequency only:
* While in TX (Mic keyed):
* Check for 8V at one side of VR7.
* If there, adjust to make sure that the TX frequency changes.
* If there and no change in frequency .... Check for bad VR7 or shorts at wiper wire back to the board connection. (But you don't have this problem if SSB is working.)
For accurate checks and adjustments make sure that you do not short any connections (especially making any voltage checks), which may cause more problems.
73