I have followed sluckeys and SILVERGUNs advice, found some old hook probes and attached them in place of the wire between the fuse holder and the switch and made current measurement
I have done about 20 power ons before the failure occurred. Just the rectifier tube was installed.
All of them followed this pattern: initial peak dropped within a second to 0.15A where it stabilised.
The highest measured peaks were 0.83A, 0.72A, 0.55A the rest was bellow 0.5A.
I would assume a 0.5A slow-blow fuse would withstand these values. Of course they were measured with a DMM so the actual peak current might be probably larger.
On the last attempt when the failure occurred the values displayed were only 0.22 A and then 0.
Using a 3/4A or 1A fuse could probably stop those nuisance fuse blowings and still give the amp some normal protection too.
I have found a 0.8A fuse in my 5E3 build, so i might give it a try and check.
A thermistor in series with the PT primary can slow down the inrush current and probably solve this problem.
I have never worked with thermistors. From what i found, i would need a NTC thermistor. If i decide to go this way, would mounting it between the fuse holder and the switch a good way to go?
I hate to sound lazy but if it only happens with a particular rectifier why not just start by replacing that?
If i had a spare rectifier at hand, that would be the first thing to do. But because I would need to order it, I try to rule out other possible causes of failure. From my pedal building history i have learned that in 99 % the problem lies not in faulty components, but in my mistakes. Of course with tubes the ratio is probably smaller.
Anyway, I will probably try another rectifier tube, if I don't find another cause of the failure.
Thanks for all the helpful messages!