Gina, here a a few comments for what they are worth. $200 to fix that dulcimer sounds like a lot of money. A new set of similar tuning machines is a little less than $20. It shouldn't take more than a half hour to take the old ones off and put the new ones on. 27 inches is not an extremely long VSL for a dulcimer, but today most folks who play chord melody style prefer a shorter VSL. Folkcraft makes dulcimers with shorter VSLs. Even if you had the pieces broken out of the lower bout sound hole, it would be very difficult to repair. Personally, I would not spend anymore money on this instrument. I'd take the tuners off, clean them as best I could, reinstall them, put on new strings, and use it to learn to play until I could afford a new one.
Ken
"The dulcimer sings a sweet song."