If you (meaning those with a blue wrench and a lot of free time) can put a F-100/150 frame under a 65 Galaxie or a Blazer / pickup frame under an El Camino - surely its "possible" to put a Towncar/Crown Vic frame under a '65 Galaxie.
The issue would seem to be how close to stock you want it to look. If you want the wheel base correct, then add stock to the straightest section of the frame you can find.
I would caution you to be very care to make sure the chassis is on a flat and level surface when you start cutting and measuring. If you weld it wrong, the body will be racked on the frame. Once you start tightening down the body mounts, it may resist, but over time it will twist and doors, windows may not be able to accomodate the stress or distortion.
just an opinion. By the way, I understand that frame fabrication shops use a calibrated frame table ensure that every thing is square, level and aligned when they weld things together. You can do it by "eye" or with varying degrees of percision with normal measureing tools.
It boils down to what I said (guessed) at first. How close to stock do you want it to end up being.