why do hi-end fuses keep blowing, while std don't?

If both the standard and upgrade fuses were blowing, the
tubes would be the first thing I would suspect and test.
Since only the upgrades are going, and especially given that
the tubes are new(not that new tubes don't/can't cause
problems), I wouldn't waste my time there. Personally; I'm
using eight(what were NOS) GE 6550A output tubes, in my
Cary's. I've had two Hi-Fi Tuning Supreme fuses go out in
the(fixed)bias protection holder(one each amp over the
course of 30 days). I'm still using Supremes in the mains,
but- though I really like the more natural presentation of
the upgraded fuses; I can't afford slightly over $90 a
pop(literally), for the bias circuit. I tried a pair of
Synergistic Research Quantums in the amps and they held
fine(didn't care for the sound). Reinstalled a Littelfuse
pair of the same value, a couple months ago and no problems.
Has anyone mentioned that Hi-Fi Tuning Supremes are rated
250V, Synergistic's are rated 500V, and many output tubes
use 400 to 450V, plate voltage? That would only
matter in one's bias protection circuit, of course.

I have Acoustat tube servo amps with lethal voltages,made in the 1970's but modiffied.
There are 4 tubes in each amp,sourced from television technology because of the demands made on such a circuit.The amps also are the source of power to charge the electrostatic panels and keep them charged, they are not just "power amps",but made specifically for the Acoustat X series.They are not a conventional amplifier design.

The amps are always "on",but in a sleep mode until I flip the toggle switches for listening, and then off when I'm done.So there's a lot of juice flowing thru those fuses.

I've been using upgraded fuses(HiFi Supremes-4) in them for two years and never had one blow on me , except when it was an error on my part.

That the upgraded fuses are blowing and the stock fuses are not would indicate to me that the stock fuses are more forgiving and the upgraded fuses are only doing what they are supposed to do-self destruct before something awful happens.
I would stick with the stock fuses and the new tubes and cross my fingers, or go back to the stock tubes and the upgraded fuses.

I am curious.
What made the most enjoyable improvement, the upgraded fuses or the upgraded tubes?
The answer to that should settle it.

"That the upgraded fuses are blowing and the stock fuses are not would indicate to me that the stock fuses are more forgiving and the upgraded fuses are only doing what they are supposed to do-self destruct before something awful happens."

You could just as easily assume that the stock fuses are doing exactly what they should be doing and the upgrades are much too sensitive or not up to spec.

I couldn't find a way to contact HiFi Tuning Fuses so I asked The Cable Company, from whom I bought the fuses:

"I think that you have hit the nail on the head. The HiFi Tuning fuses are EXACT-rated fuses while off-the-shelf fuses are +10% tolerance which means that they would actually be 2.2A out of the box. The PsVane tubes additional current draw appears to work with that window while the HiFi Tuning fuses blow. This WILL happen again with these tubes, so your hesitancy in installing the new fuses was a good thing."

They don't sell any 5x20 slo-blo hi-end fuses in 2.2A, or any other rating between 2A (what I tried) and 2.5A. While the technician thought 2.5A wouldn't be risky, I'm rather reluctant to do that.

BTW, Lacee asked whether upgraded tubes or fuses made the largest impact. Tubes, for sure. But when I had stock KT88 and introduced an upgraded fuse I did hear an improvement. So now I want the cake and eat it :-)

Good news and good luck with the cake.
It's always great when things go the way you think they should.
We should now be able to forget about HiFi fuses being inferior to stock fuse at least for protection.
The next hurdle to jump is to somehow proving they sound better than stock fuses, but just for those who refuse to try them and let their ears decide.