Yep the trick is getting out of Argentina without having the bike seized.
I recently asked (last month) while re-entering AR what would the penalty be for overstay of tourist import permit. The reply was they seize the bike and say goodbye to the bike.

Civilized countries like say Thailand just hit you with a fine ($70) and you're good to go.

But Argentina being as backwards as backwards can be you can be very creative with the paperwork just as long as the dates match up.

As far as leaving Argentina into Uruguay they are extremely sloppy.
You could easily present you're altered paperwork to clear the Immigration side and simply not give customs(who reside in a different building) the temp import permit.

Then enter Uruguay with the bike "titled" in your name.

The only glitch is if you ever wish to re-enter Argentina with the same bike and the same registration plates, the way Argentina tracks your motorcycle is with the plate number.
Ideally you would want to get another "clean" (unused in South America) plate to travel freely. Peru for instance tracks the plate numbers closely on their computers.
Argentina on the other hand is pretty much in the dark ages as far as computer records go. You can fudge the paperwork but it's only good for one exit or entry.