Why exactly do you want to go to the Amazon? Sounds daft, but 'the Amazon' the river is different to what many people think of as 'the Amazon' the jungle. The River (particularly in Brazil) is very wide (miles in places) so if you're travelling down the river on a boat you may not see much wildlife as you're a long way from the banks. You will probably see more on one of the Amazon tributaries. I've been up the river to Trinidad in Bolivia for a few days on a cargo boat - not specifically to see wildlife but we saw a fair bit. Puerto Maldonado is supposed to be very good, and as you say is on LanPeru. Alternatively I have friends who've been to the jungle in Ecuador (Where you'll be anyway) and said it was fantastic.
Of course, if you want to go down the Amazon for the journey itself then you're probably looking at the expensive flights!
Looking at your route it seems you're not looking to do much in Peru. Don't want to judge you're reasons but if you've not been before then the Cuzco area is one of THE highlights of South America and has so much to offer (not just Inca ruins).
Let me know how you solve your issues as we appear to be planning similar jaunts around S.Am