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Instead of multiple RR501's, you might take a look at a WGL V572A all-housecode transceiver (http://www.wgldesigns.com) which has a much better range than the RR501.
The extra cost of the V572 maybe lower than the cost of so many individual RR501s and you then would have all sixteen House Codes covered.I would try the centrally located RR501 first.