How about the 65 - 69 Ford Fairlane / Torino? (or Merc Montego, Cougar, etc)
The're a mid-size car that have much the same chassis components as the Mustang. Less popular, especially in a 4-door platform.
If you went into the 70's, early 80's ... the Granada / Monarch was also very similar in construction. Ford Fairmont / Mercury Zephyr? again, very similar
Yes, the Bendix "power assist" steering system SUCKED, and so did the shock towers in the engine bay. Both of those shortcomings can be remedied with an MII rack and pinion and modern suspensions.
Some models came with a 390, C6, 9" diff combination so engine swap possibilities are good. I had a 68 Torino 2-dr HT with a 351C - 4V in it, and had a lot of fun with it!
Then there were all the Nova "clones" that were also somewhat popular in the 70's?
(eg. Pontiac Ventura, Olds Omega, Buick Apollo) The badges were a little less popular but they were the same car. That may give you that one-off niche that you're looking for without sacrificing parts availability.
Dodge Dart, Aspen / Plymouth Scamp, Volare
The list goes on and on.