The first thing to check is that you have proper negative bias on the control grids of the 6146 modulator tubes. Around 46 volts is appropriate. The symptom you describe is most likely caused by low or no negative bias on the modulator tubes. It could also be caused by high screen voltage, but that is much less likely.
You may find a copy of the Valiant 1 manual here:
http://bama.edebris.com/manuals/johnson/valiant/See pages 7 and 8 for proper measurement and adjustment of bias voltage for final and modulator sections.
On page 31 you will find tube socket voltages listed.
The schematic diagram is at the end of the manual, pages aren't numbered, but it is around page 52.
The modulators are 6146 V16 and V17, check the control grid voltage on pin 5 of each tube.
Make this measurement with AC power on, but not high voltage. Should not matter whether the mode switch is set to AM or CW. (In AM the screen supply is enabled on the modulator tubes when high voltage is on.)
If you do not see a negative voltage between 40 and 50 volts, check the output of the bias supply V21 pin 4 or 5 where it connects to resistor R50, which is 1000 ohms. You should see negative 265 volts with respect to chassis ground at either end of R50.
Also check for modulator bias voltage on the tap of 5000 ohm resistor R22. You might try adjusting R22 (WITH POWER OFF) then carefully measuring the voltage on the wiper contact of R22 with AC power on, but NO HIGH VOLTAGE. Once proper bias is established, continue with adjustments per manual to obtain proper modulator resting plate current.
If no negative bias is found here, perform resistance checks as documented in the manual WITH POWER OFF and POWER PLUG DISCONNECTED and after shorting / discharging filter capacitors.
Edited to correct link to manual on BAMA site. Note: If bias is correct at output of bias supply tube and resistor, check continuity of the secondary of the driver transformer feeding the 6146 grids. An open secondary winding (infinite resistance) would not provide negative bias to the 6146 tubes, causing excessive dissipation and red plates.