This has been an interesting thread (pun intended). I have an HQ16 and experience this type of frustration occasionally. One thing that seems to help is using a Magic Genie bobbin washer. I also use them in my Janome (they come in two different sizes, one for domestic machines and one for longarm machines...but you can probably use the smaller one in both machines with no problem). I have heard that the magna glide pre-wound bobbins are also helpful.
There are two excellent online resources for HandiQuilter users: the yahoo group for HandiQuilter, and the HQ Forum (which you can get to from the HandiQuilter website...I think you look under education). The HandiQuilter staff monitor the latter and jump in with suggestions as needed.