The DC heater bridge rec in the TSL601 and TSL401 is a bit on the shandy side, and can also suffer from dry joints. (I had a Bogner Alchemist in last week with exactly the same problem).
Additionally caps filtering the supply in the TSL401 are rated at only 6V!
You need to bear in mind that rectification and filtering with a large capacitor causes very large current pulses to be draw from the filamennt winding.
I've experimented with several methods of generating DC heaters, and to be honest trying to rectify the 6.3 VA winding is daft due to the high currents involved. You are far better running your preamp valves at 12.6 VDC, which will require half the current draw. OK, you will need another winding on your PT, but of a mass producer like Marshall this will be inconsequential.
Peavey us 24VDC to supply the first 2 preamp valves wired in series in some amps. This reduces current requirements even further.
Also if a power valve shorts plate or screen to cathode it is likely that it will also break the cathode heater insulation and impose the HT on the heater supply. If you are using the same heater for the power valves and DC pre-amp heater there is likely to be considerable collateral damage. Thus generating a DC filament supply for the pre-amp valves from another transformer winding makes the most sense all round.
Re the fuse in your amp. Well it did it's job. It saved the amp from any furthere damage, as a short in the fialment supply is unlikely to draw enough current on the tranformer primary (remember it is stepped down from 240V) to blow the mains fuse, so a short could easily burnout the filament winding and ruin the transformer.
Apart from very exacting applications (eg studio gear, v-v-v-v-v-ery high gain amps) I find that referencing the filament supply to around 30VDC and using well-dressed filament wiring renders filament hum innocuous.
