Hi Matt,
I don't think you're crazy, there's so much to see and do in South America, and you want to cram in as much as you can!!
Thanks for sending your itinerary plan so far - that really helps.
This is my opinion for you to consider....
Leaving Cusco on Friday or Saturday? If you leave Friday, does that mean you won't get a chance to have a look round? If so, I'd suggest leaving Saturday then - give you a chance to recover from your trek and have a look around Cuzco, which is a great city, I loved it! There are also loads of masseuse people specializing in achey post-trek legs as well, if they are in pain!
So, I'll base this on if you were leaving Cuzco on Saturday....
I know you said you wanted to avoid the Chile route for the two reasons you mentioned, but with the route below that I'm suggesting, you still get to see Lake Titicaca, and yeah, the altitude can be problematic, but if you've already been to Cusco, that's pretty high altitude, and you'll have been trekking, so your body will be used to it. If you fly into La Paz, it's a higher altitude than Cuzco - and the flights are expensive as you mentioned, I think because it's the highest airport in the world?! So....
Sat May 23rd - bus to Puno = 6 hours
Sun May 24th - early morning boat to visit floating islands on Lake Titicaca, which takes a couple of hours (I actually liked it from this viewpoint, if you went out on the boats. The floating islands are commercialised a lot, but I still found it a unique experience...and if I was pushed for time, it would be an option if I'd never been before) Then you could get an afternoon bus to Arequipa = 5 hours, then like Martin said, Arequipa to Iquique is 10 hours and Iquique to San Pedro de Atacama is 4 hours. I would recommend staying in Arequipa a night as well, it's a great city! So if you were to do that, let's say you set off on an overnight bus to Iquique on Monday night....so...
Mon May 25th - Day in Arequipa, nightbus to San Pedro de Atacama via Iquique...
Tues May 26th - 3 day/2 night jeep tour over the salt flats....to Uyuni....
Thurs May 28th - Arrive Uyuni, and get a bus when possible to La Paz - if you get one immediately, it's 14 hours like Martin said....so .......
Friday May 29th - day to relax and sight-see in La Paz before your Saturday flight...
OR.........Fri May 22nd - bus to Puno, around midnight? = 6 hours = arrive 6am in Puno
Sat May 23rd - early morning boat to visit floating islands on Lake Titicaca, then catch a bus to Copacabana in the afternoon - night and half-day in Copacabana, so Lake Titicaca from that view too?
Sun May 24th - bus from Copacabana to La Paz, connecting to a 14 hour night bus to Uyuni
Monday May 25th - Arrive Uyuni, and start tour (I think they leave at 9am or 10am - also Peru is one hour behind Bolivia - just to take that into account!)
....so if you do a 2 night/3 day tour, you're back in Uyuni, late Wednesday - I'd recommend staying a night - to get some sleep and get cleaned!
Thurs May 28th - travel back to La Paz, at your leisure - may even have time to go via Sucre or Potosi? (Or get to La Paz faster and cycle 'Death Road'??)
Fri May 29th - day in La Paz
With this second option, you're missing the expensive flight, plus you're not doubling back on yourself, and *I think* getting to see everything you want? What do you think?
Martin, what do you think? Are my timings OK on option 2? I think option 1 is pretty accurate for timings?
I'm so jealous, I'd love to be going to Peru/Bolivia next month! I loved it!

Let me know what you think of these anyway, and we can help with any more 'tweaking'!