So, what can I shoehorn into a Fiat 124?

2004 jeep wrangler used the 2.4 4 cylinder in rear wheel & 4 wheel with a 5 speed. it's the same bellhouseing as 2.0 neon engine
There ya go! Odds are decent that was an AX-5 or AX-15 trans, same Aisin trans family used behind the Supra NA and turbo engines. Not a T-5, but just as good and perhaps better.

Re: Rotary's. Having worked around them in a racing environ for a very short bit the only way that I'd consider one is turbo'd. If only to quiet it down to something livable w/o issuing ear plugs to every passenger or needing a pair of David Clark headsets and an intercom system.