Many things can cause low volume other than OT,
A signal generator and an oscilloscope will help you determine where the signal (the sound) stops.
Essential tools for anyone working on amps.
__________________________
Testing Output transformer are very easy
I do this test on few OT with success. I find wich are good, wich are bad.
_________________________________
Testing Output Transformer and finding Impedance
Amp at OFF, disconnected from wall outlet
Power tubes removed
1- Signal generator set to 1000 hertz AC 0.5 volts
2- Send this signal to OT secondary , check with accurate meter to have 0.5 VAC on OT tap. Or close
3- Read AC voltage at OT primary
4- For exemple if you read 14.35 VAC you divide by 0.5 ( or what you read at 1- )
14.35 / 0.5 = 28.7
5- Square the result ; 28.7 X 28.7 = 829.67
6- Multiply by secondary output impedance where you are connected , say 8 ohms
829.69 X 8 = 6631
7 - This reading 6631 is the primary input impedance
If you use two 6L6 in push pull , look on Tube Book for Plate Load resistance . You’ll see you that you need 6000 to 3800 ohms for two 6L6 in PP class AB
The reading we got 6631 is on spec
_______________________________________
If transformer is no good your reading will be very far from what we should get .
By experience these test do not work on Super Reverb Transformer or other with 2 ohms Output Transformer impedance
You can do this test on unknow OT to see how / where you can use it