So you are flying into La Paz at the start of this 10 week trip? You can fly to Sucre, then bus to Potosi and if you have time bus to Tupiza and take the 4 day jeep tour to Uyuni which is what we did and is spectacular. Being in Sucre will help with acclimatizing but you should consider taking Diamox as well. From Uyuni you can fly to La Paz or take an overnight bus. If you don't go to Tupiza you can get to Uyuni from Sucre via Potosi by bus. La Paz deserves a few days. So then instead of flying to Cusco I assume you would like to see Lake Titicaca so take a bus to Copacabana and go to Isla del Sol. Then from Copacabana to Cusco you can take an overnight bus (10 hours or so). You need (at least) 2 weeks for Bolivia with Tupiza.
Then you will want 5 days in the Cusco area for Cusco, Sacred Valley and Machu Picchu. Then fly to Lima. If you have time go to Arequipa (flight or overnight bus from Cusco) and the Colca Canyon, overnight bus to Ica for Huacachina, then Paracas and Lima. If you don't have time for that you can take an overnight trip by bus from Lima to Huacachina but I would not skip Paracas (Ballestas Islands and Paracas Reserve) because I liked it better than Huacachina and I would actually suggest skipping Huacachina so you can visit northern Peru after a day or two in Lima. You can take an overnight bus or fly to Trujillo (Chan Chan and Huaca de la Luna), bus to Cajamarca, scenic bus ride to Chachapoyas (Kuelap!, Gocta Falls...), overnight bus to Chiclayo/Lambayeque for the Lord of Sipan museum. If you fly to Piura you would miss all that. I have not been to Piura or Mancora but I would prefer visiting the sites I just mentioned to going to the beach. You will want at least two weeks for Cusco to Chiclayo (that is without Arequipa, Huacachina and Paracas... add a week). I have not been to Ecuador but again, I find your itinerary a bit odd as you will miss Cuenca and Banos and the whole inland route to Quito. And if you do go to Montanita there are direct flights to Quito.
Then in Colombia, instead of flying to Cali, visit San Agustin, Popayan and Tierradentro! It would be on the way and it would be a real shame to miss those places. You have so many flights planned... Don't fly from Cali to Medellin either. Go via Armenia to Salento and the Cocora Valley. Then via Pereira and Riosucio to Jardin and then to Medellin. Or at least visit Guatape as a day trip from Medellin and Jardin as an overnight trip. Otherwise you only see large cities and not the colonial towns Colombia is known for. You need 3 weeks in Colombia for what I suggested.
So I think you have time for most of my suggestions and you can even add Arequipa and Colca in Peru. And you don't need 4 days in Cali or Cartagena or even Bogota.
When I said 5 days in the Cusco area I meant without a trek. Add a few days if you want to do a trek instead of taking the train to Aguas Calientes for MP. The Inca Trail is sold out for September but there are other treks you can do (Salkantay, Lares...) when you get to Cusco. If you want to hike a mountain within MP (Huayna Picchu or Montana) you should buy MP tickets in advance as well. Check availability (and buy tickets) here: https://www.machupicchu.gob.pe/inicio
I would take less flights and with the ones you really need wait till closer to the date so you have more flexibility.