Hi James,
You can go to an iron-on, if the structure is strong enough without the additional strength which doped covering adds and if you remove the old stuff.If you don't get most of the dope off, it may blister when you apply heat to the iron-on covering.
Removing the dope and covering can be a job----some use sandpaper; I have used lots of paper towels and acetone/lacquer thinner. Neither method is any fun. If you use the acetone/lacquer thinner, remember the hazards of the chemicals.
Cheers,
Jim