I think it can be fixed . Im not going to say this would work for sure , but what I have done rather than add a splice , is to remove a turn or unroll it enough to reconnect back to the broken wire . This way you only have 1 solder joint instead of 2 and it is easier to reinsulate the area again . I have never done this with a HV trans but have done this with other transformers and and field windings in electric motors and had exellent results . Thought
I would pass it along .
Best of luck with it , its a neat little set
Murray