It should work, I think they used a 5763 to drive a pair of 6146's in lots of rigs, with drive to spare.
Measure the plate current on the 5763, see what its doing.
Screen voltage on the 5763 might have an impact on the grid drive.
You might try changing the grid circuit Q, maybe try a bit more or less coil there.
If the Q is too high, losses in the coil go up and tuning is touchy.
The more grid leak you use, the more drive you need to get the same current.
Since I drive all my rigs using the flex, or the 32V3, I have lots of extra drive power to waste going deep into class C.
I dont have books with me, but what is the output power of a 5763, and what are the drive needs of a pair of 1625's?
Gito would tell you to put in an 813 as a driver, as you need 3x the power to drive the 1625's.
Brett