How much closer are we talking? If its a matter of a fraction of an inch, you can easily tune back the bridge saddles, especially if its the old three-saddle model. Even the more modern ones can be pulled back to a degree.
I learned a trick about a Bigsby installation that might be able to do the trick for you. Take the new Tele bridge, and run two pieces of kite string through the body for each E string. Your bridge pickup will be out for this, but you'll still have your neck PU in I'm assuming. Make sure you have something tied to the end of the string to simulate string ends, and then string the two strings in through their appropriate tuners. Align the strings to go past each of the end pole pieces on your neck pickup. I know on the neck, you're never "perfectly" over the strings, but this will ensure that you don't have one string hanging way above or below the pickup. When you've aligned everything, take a tape measure out and tune up each string till its exactly 25 1/2" from the inside end of the nut to the middle of the saddle, where the string will make contact. Use slight pressure on the bridge to ensure things are tight. You don't want to stretch out the kite string, but you also don't want to have things slopped around. When each string is at the appropriate length and is seated well enough over the pickup, use a pencil, grease pen or what have you, and trace out the brige. This will allow you to take the saddles out in order to drill new holes if needed.
The best piece of advice I can give you on this is GO SLOW!!! Nothing is ever worth rushing, and you will just wind up being pissed off at yourself if you rush through something.
Lotsa luck!
