I dont even bother with average output readings. If you want to see higher average power, back off your modulation level with the AMC pot, and watch the average rise a bit. As for RMS, that doesn't even apply to rf power readings other than as a (possibly interesting to someone somewhere) math study.
As for that coil, assuming you are using a pure 50-ohm resistive and non-reactive dummy load (NO wire-wound resistors!!), then you need to inject a steady tone of around 600 or 700 mhz, maybe 1khz, to have a solid modulated signal before you can tune that slug. There WILL be a single point where it has max output within the band you wish to tune for, and that point will be somewhere in the general middle of its tuning range. I think the tops of the slugs most of the ones I tune end up being a couple millimeters down from the top edge of the coil shell, give or take a bit.
As for the power meters you mentioned, I am not familiar with them, so I can't comment on accuracy. However, if you DO have a supply that delivers 14 STEADY volts to the radio, and you STILL only see 120 watts, there has got to be a measurement accuracy issue someplace, or a problem with the radio(s). At 14.1 volts I see a MINIMUM of 150PEP after tuning, and I can't remember the last time I saw one lower than about 170-175. Most tune out to 180-190 on my Bird 4314B meter, AND on my
Wavenode system. This level is also confirmed from the Bird carrier reading and o'scope calculations.
Try this: Place a fast-responding volt meter at the power cord inout to the radio, and watch the supply voltage as you're transmitting. See if its actually keeping the voltage at the radio at 14. If not, run larger cable to the radio from the supply. You may end up needing to rig a remote voltage sensing circuit for tha power supply to make sure it keeps the actual radio voltage at the 14 volts for which you set the supply.