If it was me, I'd go buy a cheap junkyard starter and try it. The only time I had a starter click and not turn, engine was stuck, bad battery or starter. Sounds like you ruled out 2 of 3 for sure.

68 Road Runner, 69 Belvedere, 71 Challenger Vert
340 barracuda, 01 Ram CTD, 95 Ram, 04 Ram, 85 Daytona turbo Z
66 GTO, 06 Magnum RT AWD. 07 Ram CTD, 07 Ram