The method you've used is similar to ones that FOREX traders use to value traditional currencies, which would speak to its validity. A market-basket of goods is defined, and a relative exchange rate for two currencies is based on the price differences of the two market-baskets.

A potential issue with this analysis is that your market-basket only contains illegal items -- however, even if your final valuation isn't accurate, it suggests to me that there are likely other cross-market pricing inconsistencies. I assume those are what you're interested in finding.