I wouldn't bother replacing the output transformer, you can generate 60Hz and measure the input vs. output voltage (AC) to see if the ratio still looks good.
The 25C5 is drawing a pretty healthy amount of current, and it looks like you have ~254 Ohms of resistance on the primary of the output transformer, which is generally a good sign.
Looking at the 25C4 datasheet, there's an operating point that is 110V plate, 110V screen, 7.5V bias, 4ma screen current, 50ma plate current.
This isn't horribly off from your datapoint, the decreased screen voltage will raise the gain slightly. With the book operating point, you get 1.9 watts output, which would be 3.9V into 8 Ohms (2.75V into 4 Ohms), but with more voltage needed at the grid of the 25C5 to get you there (the output transformer step-down isn't helping).
You could have a bit of a dead 25C5, did you try another? If you dropped the screen voltage even lower, I would expect gain to go up bit. Also, a ceramic phono cartridge can have in excess of 1V of output, which would not require much voltage gain from the 25C5. (Frankly, if the ceramic cartridge was removed and replaced by a moving magnet cartridge, you'll really spin your wheels trying to get the player to work properly)
