The recently inserted schematic shows that you have a big inductor with DC current. That DC will not stop suddenly if you try to break it, but generates as much voltage as needed to decay gradually. It's seen as voltage peak in the primary. The peak is as high as needed to let the current continue as an arc in the switch and die gradually as the inductor energy is dissipated.
A fix: Insert a diode between the left end of the inductor and the GND. It doesn't short the DC voltage if the cathode is up. I would try it at first.
The inductance doesn't suddenly sink more current, the arc only lets the current decay gradually. The arc can be so big that it shorts also the mains AC - that's your current peak. The suggested diode allows the inductor current to decay with no generated extra voltage => no arc.
All parts which are in parallel with your transformer to the right from SW1 enjoy in your current system a voltage peak. You have been lucky-the insulation in the transformer is still OK.
There may be certain non-technical, but decisive reasons why no semiconductor parts can be included. That excludes the diode (except if you can insert a tube). Another idea is to insert a RC series circuit in parallel with the transformer primary.
The capacitor must be so big that it can contain the energy of the inductor (= 0.5 * L * I^2) with low enough voltage to prevent arcing.
The capacitor has energy 0.5 * C * U^2. As reversed U=sqrt(2 * energy/C).
The resistance must be so big that the current peak isn't too high for the switch nor fuses when the amp is turned ON. It must be small enough or it can neutralize the effect of the capacitor. The max primary current * R must be lower than the arcing limit voltage in the switch. The resistor dissipates energy continuously from the mains AC. That must also be taken into the account.
It's well possible that a good compromise doesn't exist. More possibilities:
- new design
- mask a diode to look some 100 years old component. It must still be documented!
- have an old style light bulb in parallel with the transformer primary. One made for an electric oven can do the job (a guess, not calculated). Obviously the heaters of the tubes connected to other windings are far too light load to absorb the pulse.
- have SW1 which has the halves in separated spaces and far away from the protective earth (the arc occurs but cannot make a short). One pole switching makes it easier to achieve.