The FX 140 is a solid ski, and I've never heard of your particular problem, but it is possible. It is definitely not worth doing a $6000 repair.
You can get a rebuilt engine for around $2000, but it is a fair amount of work to install it.........I'd guess a dealer would charge $1500+ for the labor. If you are mechanically inclined and have an engine hoist and the tools, this is the way I'd go. Used engines are hard to find, but that is another option. If you are going to have to pay someone to do the work, I think you may almost be better off parting out the ski........lots of guys are looking for parts, hulls, etc., then using the money to buy another ski.