Will Origin Live Conqueror tonearm fit my Rega RP10's skeletal plinth?

Yes. That's what it says in the instruction manual. It's a pain, especially that fine adjustment peg. 

Hopefully you'll hear noticeable SQ improvements WITHOUT doing any modification/harm to the plinth, which will affect resale value.

So far, doesn't sound like a smooth transition. 

Did a lot of listening, breaking in today. I noticed that the arm height was sinking. Found that if I tightened the large nut beneath the plinth and the VTA adjuster clamp sufficiently, movement of the arm body was minimized and height/VTA could be maintained. This is somewhat against the advice OL provides in the instructions which suggest finger tight should be enough, but finger tight doesn't hold on this plinth. So far, and this is "early days," sound quality is about the same as the Rega RB2000. 

Will update in a few days.

Glad you are starting to get things situated.  I am currently using a Conqueror Mk4 and an Enterprise Mk4 and my dual arm Origin Live Sovereign TT.  In the past I have also owned the OL Silver Mk2, OL Encounter Mk3c, OL Illustrious Mk3c so have a little experience with your situation.  The “finger tight” requires some pretty strong fingers, but know that you should not ever need to employ any wrench. It must be just tight enough that no rotation of the tonearm base is possible during general use.  My normal procedure to accomplish this is to get the nut very tight by hand with the tone arm rest slightly to the right from the final position I wish it to occupy.  Tighten the nut as much as possible under the table and then hold the nut and slightly rotate the tonearm base above clockwise ultimately placing the arm rest into its desired position.  Rotating the base above while holding the nut gives one a little more firmness.  These are very small adjustments.  Snug it just enough until the arm does not rotate while you are setting the other adjustments or when in use.