The suggestion of removing either of the two 5675 pencil triodes from the osc/amp assembly is a very bad idea and as I previously stated should be a last resort. First, there is probably a 0% chance you can find a highly specialized tube tester that could test them, they aren’t your usual plug-in tubes. Second, in circuits like this, manufacturers generally will say not to even test tubes because if they work in the circuit that is all you’re interested in. Plus most tubes will work well outside of what a tube tester will say is weak or bad.
As I said before, the best way to check the tubes is to check the supplies feeding them plus, in this case, the R.F. output meter. The question I’ve asked before is whether the output to the meter can be adjusted to the set line and is that reading stable. The manual states the meter is reading the voltage at the input to the attenuator so if the meter indicates proper output, forget the tubes. If the meter indicates properly the problem is external to the osc/amp assembly and messing with it is a good way to really screw the HP 608 up beyond repair. The HP608 was calibrated after the tubes were properly installed and even moving some of the connections at these higher frequencies could really change calibration. Checking the filament voltage and current then checking the B+ will check the inputs to the tubes and the meter will verify the output.