I am ill just reading this! My d is a flautist and her flutes are so much a part of her! I would speak to a lawyer only because there is a difference between verbal and written agreement. Although it does seem they are being extremely cooperative, I would just make sure. You never know what might happen if they have to replace a 6 - 8,000 dollar flute.
Also, we have additional riders on our d's instruments. Homeowners will cover only certain losses. Are you comfortable with the person who is repairing the flute? This person should be able to tell you if he feels he can get it back to original playing condition. I am told that the mechanisms in Japanese flutes are so incredibly precise...you do not want to compromise that. We deal with an absolutely wonderful person in NY. We completely trust him with all d's woodwinds.
Your d must be going through so much now. I hope this all can be put behind her so she can move on. However, I know it is hard when there is not only the bond that an instrumentalist has with their instrument, but also an emotional tie to how they actually got the instrument. My heart goes out to her...my d would be devasted. I cannot even imagine.
My husband and I are also non music people. But we have two musical girls!!!! We are often asked where their talent comes from, and I have to reply....not from me! I will be keeping an eye on this thread. I look forward to seeing that everything has been taken care!!!