OK, to answer your original question in general, you would rewind the primary with wire 40% larger in diameter and use 55% as many windings, give or take a few. I don't think regular electrical tape would be appropriate, something stiffer and higher temp such as you mentioned. I've never glued a transformer back together and I'm not sure how you will get it apart, but I would try a potting epoxy. Rewinding in place sounds difficult, but I'm still not sure what your transformer looks at.
I have an 858D clone (SumSour to be exact) and I only see one very small transformer inside it. Taking a close look for the first time, I see no voltage or power spec labels anywhere on the unit! And it isn't clear to me that the little transformer is a mains unit. I can't imagine rewinding it unless you are a jeweler or something. Could you post a photo to see if your unit is the same inside? And tell us how you got those voltage specs you listed.