I'll share a few additional details about our trip. There were many "firsts" for us on this trip, which means I'm no expert. For what it's worth ...
We flew from CLE to LIM on American in Business. I scored one excellent award seat right off the bat (using BA Avios), but there was only one and I never did see another come up. NEXT TIME we will fly on separate flights if we can. Anyway, I took an American anytime "award" for the second seat for too many AA miles. Still, I was happy. The flight times were as close to ideal as you could ever get and lay flat seats! Of course, American canceled this flight and rebooked us on one with crappy times. But we got there.
We flew back in Business from Quito to Washington DC for an overnight++, then on to CLE. This on United Business awards that were reasonable. Layover too in Panama City. Normal straight back seats, tho, on Copa. Made use of the time before our next day flight out of DC by stopping in the Air and Space museum attached to the airport. Very cool! A negative turned out to be a plus for our overall 25 day trip!
Flights from LIM->CUZ and back and then LIM->UIO/Quito were super cheap awards (coach) using Avios (and switching some things at the last minute as described above, still cheap with Avios). I did not see Awards to GPS/Galapagos via the BA website (which is where this article would have inspired more creativity). I ended up getting a LAN credit card early for the points and (noting some drama described above) this paid for MOST of our RT to/from the islands.
There is a Ramada attached to the LIM airport that is adequate. We used Wyndham points for one night when we first arrived there, very late. We paid for a night transferring from CUZ to Quito because of timing. Mixed results, but it is a handy resource ... although I would find something better when actually STAYING in Lima. We spent 4 nights in the Miraflores Raddison on Club Carlson points (2 nights free, I miss that benefit).
It was a great trip. I hope you have as much fun as we did!