The aftermarket headers prove the chassis is very similar, because getting long tube headers to snake around a chassis' hard points and unique bits (like steering and brake systems) takes a lot of engineering. The passenger side header fit just like a Torino, but the driver's side had to be modified to clear the Mark/Tbird steering system. So no, they aren't identical, but they are quite similar (wheelbase aside). There is no modification needed from 429 to 460, it's the same motor in terms of bolting up a header to the exhaust port of a 385-series Ford engine. All headers for these motors (Boss 429 aside) interchange, it's the chassis that becomes the sticky bit.
I am splitting hairs here, but the 1972 Thunderbird didn't have a 460, it had a 400 or a 429. The 460 was another unique bit reserved for Lincolns at this time. (That changed circa 1974.)
Agreed with your assessment of badge engineering, the issue here is that the Mark IV was indeed more obvious (good phrase) and paved the way for future grievances like the Versailles, Mark LT, and Zephyr/MKZ.
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