That is really unusual to have two heater circuits. Is one rectified and smoothed and not the other? If one is rectified, and or smoothed, then you still could use a 6 amp or more rated transformer. It is always an upgrade to rectify and smooth the heater supplies. It causes less noise and makes the tubes last longer.
That high tension winding is very low current draw. That would leave virtually no margin and is probably the reason for the failure. I guess junk products have always been with us and I guess always will be.