This may or may not help you as anyway you go, as E-bodies are expensive compared with Ford and GM, but the least expensive E-bodies are the “post performance” models of 1972 to 1974. Since your goal is to add a modern engine to a classic car, the lack of big block engines and the introduction of low compression smog motors in 1972 shouldn’t be an issue.
Although the higher performance of the 1970 and 1971 models factor heavily into the increased premiums, there were also significant changes made to the appearance in 1972 which make them less coveted and expensive. The Challenger has the “sad mouth” grille, and the Barracuda received a grille that is a blend of the 70 and 71, but not as clean as a 70 and not as mean as a 71. The side marker lights were also no longer flush with the body. 1973 saw the introduction of 2.5 mph bumpers, which were simply reinforcements placed behind the bumper moving the tucked in bumpers away from the sheet metal, and the addition of large bumperettes front and rear. The bodies however, are the same and have those classic lines.
I opted for a 1974 Barracuda. Hey, at least all the post performance cars came with front disc brakes and sway bars (I think)!