I would expect that you'd join the second partner's program, then have the outbound flight in each case credited to your AA account and the return on this new partner account. (Make sure the promo for that carrier permits non-residents of their home country to participate, something CP does not do from what I've head in another strand of messages.) Also, ensure that your non-AA carrier's account number is printed on the boarding pass to ensure credit has been changed from the one you used to get there.
I assume each of your round trips in on a different oneworld carrier so you can use my solution. I am note sure an AA codeshare on a CP-operated flight would be counted as CP...
Also, as someone has already pointed out, QF's program is measured in kilometers and not miles, so 100,000 kms is worth a third less than 100,000 miles. This means you can't get quite as generous a reward on QF as on the other partners using miles.
Maybe you can show us your planned itinerary and where your base airport will be. You say most of this will be in Europe, so I assume you'll fly AA to LHR, then BA, IB and Finnair, then do a transborder up to Canada when you get back to the US. Do you plan QF or CA?
As for connecting times in Europe, this could be dicey more because of air traffic control problems that have plagued Germany and Spain particularly, and all flight flying over them. (I flew in France, and to/from UK, over the summer and experience no such problems, fortunately.)
Customs and immigration would be an issue passing through Heathrow (as would terminal changes and security checks) and again when you make your first entry into mainland Europe.
Once in the European Community, there will be no customs or immigration to deal with until you leave the EC again. Thus from Spain to your connecting point to Finnair (for example, Paris, Frankfurt or Amsterdam) will be no problem, though I can't recall if Finland has joined the EC, so you may have to clear customs and immigration to return.
60-minutes most certainly will NOT provide you with a safe connection. And as I noted with ATC problems, even 90-minutes might give you ulcers. I'd be conservative and recommend 3-hours minimum. (If you're elite on AA, use the privilege to sample the other carrier's lounges. They won't charge you for alcoholic drinks either.)
Let us know how you ultimately plan to do your trip.