Most transformer windings are sealed in varnish. Dewinding them can be a real problem leading to a broken wire. The other problem: if it is a center tapped secondary, one of the two sec windings is on top of the other. If you dewind the top one, it will unbalance the center tap point. Instaed of a 17V-CT-17V secondary, you will have a 17V-CT-14V winding so it is no longer center tapped.

 

If you dewind the top one, it will unbalance the center tap point. Instaed of a 17V-CT-17V secondary, you will have a 17V-CT-14V winding so it is no longer center tapped.

This can be overcome by winding Bi-filar.
I have done a few EI transformers in the past, but they a pain to dismantle and re-build.
I usually stick to Toroidal now for that reason.
Max.