I don't think there is any explicit requirement of PP validity like you mentioned. In the PPR mail/email, it just askes to be valid. IMMIGRATION VISA is a single-entry visa with sole purpose of landing and is normally given up to the validity of your medical result. And IME reports are usually valid for 1 year (12 months). For example, if you did your medical in Dec, 2011 and they stamp your PP with IMM Visa in May, 2012; your medical resullt would remain valid for another 7 months (12 mo - 5 mo). As a result, you would most likely to get IMM Visa valid for this 7 months. So, they will just check if your passport is valid for the rest of the process (mailing PP back, landing). I hope I made it clear.
Re; your new passport, your plan seems good to me. Staple both passports well. When I went for new PP, my embassy stapled both together by themselves as my expired one had valid US visa. I also use a rubber band to hold them together.