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There was a recent post by Weasel relating to mentoring.
I guess my question would heve been better placed there, but that thread is now closed, so I missed my chance.

Would it be possible to have a scoring system that takes into account the starting scores of both players?
I believe competition chess works in this way: you get more points for beating a more experienced adversary than for beating someone at your level or lower.

Does anyone else think this is a good idea?

It's already there, the ELO rating. If you go to the ladder you'll see it at the top of the table. Click on ELO and you'll get the list sorted based on highest ELO instead of highest total point score.