(1) Welcome to CT!
(2) I'll be blunt and to the point ... Nope, it can't happen - not unless you're willing to invest in a lot of custom surgery and fabrication that will end up costing a lot more than the truck is worth (and probably reducing its carry capacity for haulling your show bike).
The 6-lug (4X4; PreRunner) suspension is a whole different setup from the 5-lug (2WD mini) setup. These differences run all the way down to the frames and attachment points.
If you were to want to preserve the 4WD capability, the whole transfer case / front driveline stuff would need to be heavily modified just to make room for the general drop.
Even if you'd be satisfied just to drop the 4X4 a couple of inches with different springs, etc., there'd be a lot of tweaking necessary to keep the front driveline.
Even if you'd start with a 6-lug 2WD PreRunner, there'd be a limit to how far you could lower it without getting into frankenstein fabrication / mods.
You indicated you expected the "cheaper to swap it out for a 2WD mini" advice, so I won't push that angle (though it's still the fact of the matter).
Your best and most economical option is to shift your focus and work on ramps (whatever) for getting your show bike into the bed of the 4X4 you already have.
That's it in a nutshell.