This is all hard stuff.  Homeschooling I tend to be pretty laid back.  But I do require the kids to be challenged and engaged for a period of time every day.  And that does include music lessons for them.  Music lessons can be great for GT kids, but if it's not their thing, I think that's fine too.  
I think the thing that really comes to mind is that it is a marathon, not a sprint.   My kids are definitely kids that would be happy to coast.  They do need to be encouraged and prodded, to try new things.  I back off if something isn't for them.  I am seeing some encouraging signs in my 9 year old in terms of self motivation.  But it definitely wasn't an overnight thing!  To me it sounds like you are doing a great job giving your child outlets to challenge themselves.