A permanent backstay to the masthead on a fractional rig
to complement the running backstays is not uncommon. Don't mistake "flexible" for "weak"! Just because your mast tip is bendy doesn't mean it will break. It will easily hold the mast up! Of course you can break the top of the mast if you really load it up. On the drawings I am looking at for the IMS 40 it appears to show a masthead backstay already. Is that not the case on your boat?
Farr IMS 40
As for repairing a mast, what you are describing is called "sleeving" and it is acceptable on cruising masts. On a flexible racing mast like yours it depends on where the break was, because that repair
area could change the bend characteristics of the mast in a big way. Most race boats would opt for replacing the mast section for that reason, but they are also covered by insurance.
Another option for stabilizing your mast might be to relocate your chainplates aft, and sweeping your spreaders aft. I had a small race boat with a very bendy fractional rig
, and it didn't need a backstay at all due to the aft swept spreaders. Of course it was a much simpler mast than what you have.
Keep in mind I am not a rigger, I am simply relating mast configurations that I have sailed with in the past. What you have is a very complicated high performance mast. Unless you really know what you are doing, be very careful what kind of modifications you do! It is unfortunate that you do not have any professional riggers in your area. Are there no high level racing teams in korea that could tell you who to talk to?
P.s. If you do end up buying a new mast, I have heard of people retrofitting the old IMS 40 mast with the newer and simpler Farr 40 rig
Of course you could just train your crew better! Especially the runner guy!