What are the minimum requirements for a student to solo a second make and model aircraft?
As long as your training has been done in the same category, class, and type as the aircraft you are switching into, the FARs aren't specific regarding repeat training required.  Instead, this will fall into the realm of flight school policy, and CFI judgement.  

For example, if you are transitioning from a high wing to a low wing, or from manual to electric flaps, your instructor will need to ensure that you are safe and comfortable flying the new aircraft before signing you off to solo.  To the first question, it is almost a 100% certainty that you will at a minimum need to complete a presolo exam on the new aircraft to ensure that you know the systems, airspeeds, etc.

If the instrumentation and navigation equipment are similar enough you probably won't need to refly any cross country flights, but again this is at CFI/Owner's discretion.

You will, of course, need a new solo endorsement for the specific make and model.

And don't forget the most important piece, two weeks before your checkride YOU need to be comfortable in the aircraft you will take your practical exam in!  Don't short change yourself, push out the checkride if needed to make sure you are ready.

The best advice is to consult your CFI and/or the flight school chief pilot to put together a re-training/recovery plan to transition.  Good luck!

ADDENDUM:  I see in your profile that you are a CFI with 20 years of flying experience.  What gives?!  (downvote for what I perceive as deception...)