Sounds like you are using the original Dynaco circuit. A fine choice. It was originally designed for EL34 or 6CA7. IIRC going to 6L6 tube family results in lower power output with more distortion. Running the bias lower than the recommended 1.56VDC for any tube will result in higher distortion. But, many say they cannot hear it.
EH EL34 is a good choice for the original Stereo 70 because they extend the top end and are lively. Some other EL34s are more laid back and rolled off up top in the original Stereo 70.
The output transformers should not have to be changed for the tubes Dynaco originally allowed. The alternate power tubes mentioned in the original Stereo 70 manual are 5881 and KT66, provided they can be biased, which is another issue. KT88/6550 was never recommended by Dynaco for the Stereo 70.
With regard to the original power transformer, there has been much discussion as to whether it is adequate even for the original tube complement, but as long as it does not buzz or vibrate excessively and is not blowing the 3A fuse, it should be fine.
With regard to KT77, they are often spoken of as a drop in replacement for EL34/6CA7, though Dynaco did not mention KT77 in the manual. When I used KT77 in my Stereo 70, things definitely ran hotter, temperature-wise. There are beefier power transformers available from Triode USA and dynakitparts.com, which are considered a general upgrade. But, again, if you have the original Dynaco power transformer and it is not making too much mechanical noise and not blowing the 3A fuse, I don't see why it shouldn't work fine.
As for sonic differences, some folks use 6L6 types (including KT66) in the Stereo 70 and like it a lot, even though measured distortion may be higher. Again, a practical concern is being able to bias them.
For 6550/KT88, an upgraded power transformer would probably be a good idea, though I would question compatibility with the original output transformers.