Field coils can be a pain to fit without the 'right' weapons (mini-jack, wheeldriver, whatever, as per the literature).
However, with an E3L it's not so bad if you use 2 lengths of 5/16th BSF studding and nuts to haul the pole piece up to the yoke in gentle stages, having warmed the coil with a hairdrier beforehand to help it assume the necessary shape. When flush, put in new pole shoe screws, do 'em up good and tight and all should be well. You'll even have unchewed slots in the screw heads if you use a good-fitting scrooge.
For getting the screws out, I and many others use a large centre drill and simply take the c/sunk heads clean off, leaving the dyn body unmarked. The rest of the screws will come out of the pole piece easily afterwards. A chunky centre drill won't wander . . . . Far better than hitting things with impact drivers, chisels etc, which risks damage to and distortion of the yoke.