Agreed.. sounds like the last cook deteriorated the laminations.
You really do need to check your line filter and you need to check your bridges.. Once you are sure these are OK you can add a transformer to the line. What are the outputs required?? If 24V is one, then its possible to get a 240V-24V transformer and attach etc etc.. last thing you want to be doing is cooking more game transformers.. we need to get this fixed. The smaller transformers are pretty cheap and you can afford to experiment a bit to source the fault.
See how you go with the tranny unplugged and we can go from there.
Basically, you shouldnt blow any fuse with no outputs on the transformer, theres no load and so the only current flow would be from the internal resistance of the windings, unless of course you have a shorted line filter or delaminated windings... the current draw on the primary side of the transformer is small when the game is on.. transformers are brilliant at converting AC extremely efficiently and then fanning out the power.. a 2A primary draw on a transformer is 480W or thereabouts.. thats a lot of 12V.. or 6V power.. in fact will give you 80 Amps at 6V.. so you see that the primary current need only be small... 1A would be too small.. 3A may be too much.
Need the results of the line filter!

Thank you kindly for the perseverance with me and helping out, as well as everyone else that has helped out with advice. I'm going to call it a night now. It's getting late and it's cold out in the garage (winter is coming....). I'm going to test the bridge rectifiers tomorrow night as my next port of call. As for the line filter, how do you test a line filter?

Cheers!
Adam.