I am guessing it only pushes the treble side toward the bridge. You may want to measure on the bass side...my guess is that it will be a bit longer than 628. If so, that may be fine. As long as you can get the bridge saddles to adjust sufficiently to intonate it should be fine. One some guitars you actually see the bridge set a little farther back on the bass side than on the treble side for easier intonation. All that said, you should be able to set the neck an mm or two in or out without too much problem if you must.

I would fill any gaps with veneer because it's easy to build up to whatever thickness you like about 1/2 mm per layer. You can make a wedge out of veneer by cutting strips; more strips at the thick end of the wedge, less at the narrow end. If you wanted to add a bit of to push the neck back, two to three strips at the pickup end of the neck pocket would put it in just about exactly the right place.