Even without measuring, I can tell you "very strong" is probably not normal. Let me know when you've measured it.
By comparison, I have 98 dB speakers. From 8 feet away, I can't hear any hum, from 4 feet away I can begin to detect a little, and with my ear at the speaker I can hear it clearly. It sounds like your expectations are realistic based on your experience with tube amps, so I think you should be able to achieve a satisfying, but not altogether silent result.
My amps don't have isolation transformers, snubbers, or anything else other than what you see in the schematic I posted so, the question is: What's different?
Please start by telling us what you've done to the amp since you last reported.
For example:
1. Did you move the power resistors to the outside of the enclosure, or are they still cooking the transformer inside the chassis?
2. You mentioned something about using an isolation transformer. What did you mean? Audio isolation? AC mains isolation?
3. You mentioned your transformer is 800VA. From the pictures, it appears to be about the same size as my 400VA transformers. Out of morbid curiosity, what does it weigh?
4. 95% of my "mystery" hum problems, come from faulty construction, bad connections, bad solder joints, messy wiring. Have you gone through all of your connections?
5. What color are your speakers?
I'll check my notes later, but as I recall I measured <100uV noise, and Part Deux was 30uV