"Full-power testing" of a 12AX7 is usually not relevant, since that high-mu triode is used for high voltage gain and usually not driven to clipping. A medium-mu triode such as the 12AU7, running at higher plate current, is more likely to run closer to clipping.
If you can run a very high plate load resistance, or constant-current source plate load, then you can measure the amplification factor "mu" directly as the voltage gain: it is reasonably constant over the useful range of plate voltage and current with small signals. If you saw 60 V pk-pk at the plate with 1 V pk-pk at the grid, then you need to correct that gain for the series combination of Rp (see below) and Rload to calculate mu, which characterizes the internal voltage source in series with the plate resistance.
The other independent small-signal parameter is the transconductance gm, which requires a very small plate load resistance (ideally, a short circuit). It is the ratio of the AC plate current divided by the AC grid voltage, and is a strong function of plate voltage and current. Measuring the AC plate current can be done with an appropriate small plate resistor, so long as the voltage supply is constant (no AC component).
The third small-signal parameter is the plate resistance Rp = (mu)/gm, and is therefore also a strong function of plate voltage and current.
For American tubes, the GE data sheets in Frank's website are usually the best source of information.