Tube mixing

Here's the problem with different tubes on one side of a push-pull amp.

I assume you're familiar that a push-pull circuit divides the signal into two halves (usually shown as a top & bottom referenced by a center line), amplifies each separately, and rejoins them at the output.

Using a simple sine wave input where the top half of the wave is a mirror of the bottom, a 6550 tube is going to have "X" amount of gain while the KT88 or KT120 will have a different amount. At the least, your output push-pull wave will no longer be a more powerful duplicate of the input push-pull signal. You will have distorted the wave.

Depending on circuit design, this could also make the amp unstable.

Even if the amp is designed to accommodate all the tubes involved, I wouldn't recommend this kind of mismatch unless the situation was desperate (i.e., an audience waiting for a performance and no other possible way than this for the show to take place).

...but it seems to be a way to get the advantages of different tubes ALL AT ONCE!

That's one of those ideas that sounds great if you say it fast enough.

Rather like deciding your next car should have an 8 cylinder engine with 4 cylinders from a Chevy and 4 from a Ford to take advantage of the strong points of each.

That's usually not a good engineering approach. ;-)