The drain should be very near the power supply voltage if its dropping its either a
problem with the meter going nuts from RF (They do that!) or your power supply
The gate voltage for the final will vary from device to device for a given drain
current. I've seen 2-3V typical across a lot of IRF510s (I use them for a lot of stuff).
Other reasons for increased drain on TX is, final is oscillating, or carrier leakage.
The latter can be due to an error around the NE602 (U3 on some schematics).
If the device is unbalanced due to a misplaced part of other short or leakage
it will emit carrier and that will show RF power (maybe milliwatts) output and
increased drain. Also if the carrier frequency adjustment is way off you may
not be on the edge of the filter pass band and instead you can be inside the
passband. That can also contribute excess carrier at output.
Just a few thoughts.