[Mal Fuller]

Steve,
It seems to me there used to be a width boosting product on the market which plugged into the damper tube socket and the damper tube plugged in turn into it. The result was boosted width. If I recollect correctly, this gizmo had a capacitor inside that connected between the damper tube's plate and cathode. I don't believe that I ever knew the value or voltage rating of the device's internal capacitor.
Maybe this memory of mine will jog the memory of someone who can recollect some more details.
If I had a set with such a rare flyback and stubbornly persistent width problem, I wouldn't be afraid to experiment with an added capacitor's capacitance using temporary capacitors that have a relatively high breakdown voltage.
Incidentally, I think your Sparton was once offered for sale to me as a source for a 15GP22 for a CT-100 that I once had. I couldn't see destroying one historically important TV to fix another historic set, so I passed on it. I just found my 20 year old note where I thought it might be - it says "15GP22 Dan (847) 823-2379." It's a very cold trail I'm sure but white pages.com reverse lookup say it belongs to Daniel L Gustafson of Chicago, Illinois.
I now see your set came from California, so the one once offered to me is probably a different Sparton. Someone might try calling Dan to inquire about the set. Not much to lose.