Theoretically, the 2.4 turbo from a PT Cruiser or an SRT-4 might work too. Its the electronic giblets that would be the tough part. I hear tell if you start with a 2.2/2.5 block, that the heads from the 2.4 are a relatively straight forward swap. That gets you a 16 V, crossflow, DOHC head that should be pretty comparable to the Lotus-designed head from the Turbo III. Even better is if you get the turbo 2.4 head since its supposedly a little beefier, and it has those added oil-squirters that keep everything lubed up good.
Either way, hats off to you if you pull this off! The Rampage is a VERY cool little rig and it seems a natural candidate for a worked up turbo plant!