My $0.02:
There are so many factors that go into tube amp tone.
Lets just say your amp had a 1000W amplifier, you'd probably never get to crank the amp up and get any breakup from the power tubes. If the power amp was perfectly biased and properly designed so the incoming signal remained only in the tube's linear region, there should be no noticeable tonal coloration done by the power amplifier tubes. All the overdrive would have to be derived from the preamp section.
In lower wattage amps, lets say a Champ, you can crank up the volume and reach the non-linear regions of the power tube, which will clip the incoming signal; soft clipping at first, turned into harder clipping. In this case, you are hearing more of what the power tube has to offer and it is altering the sound instead of just making it louder.
With that said, if you are deriving your overdrive from the power tubes, you are more likely to hear tonal differences between tube types than an amp like a typical Mesa that uses cascaded gain stages in the pre-amp to create the overdrive before it even hits the preamp tubes.
I'm not sure how easy it would be to set up on your Electra Dyne, but one trick amp moders in the 70s did was to have 2 sets of different tubes in an amp. If done properly, you could have EL34 and 6L6s running together and balancing each other out.