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Saturday is going to be very tight if you need to make it to SLC. That's about a 5 hour drive from Moab. It's not really wise to drive on the small highways at night due to the open range - you might be able to make it to I-15 at Spanish Fork in about 3.5 hours.
Sunday, it's about 5 hours to Bryce from SLC. There's plenty of lodging along the way. I've stayed in the New Western in Panguitch - it's nothing great, but it's acceptable. If you are running late, there's a few places in Beaver and that would really be best if you are again driving at night. Figure about 2 hours from Beaver into Bryce via UT-20.
If you are going from Zion to the North Rim, your only real lodging options will be in Kanab.
From the North Rim to LV, you need to go back to Fredonia, take AZ-389/UT-59 to Hurricane and UT-9 to I-15. You are looking at about 5.5 hours and I would definitely try to make it to Hurricane by dark. That's going to be about 3 hours.
Out of LV, take NV-160 to Pahrump, then Bell Vista Avenue to Death Valley, go through DV to US-395 to Lee Vining to go over Tioga Pass. That's going to be about 8 hours plus any time sightseeing in DV. There are a couple places to stay in Lee Vining. Your best options are in Bishop, but it's about an hour and a half before you get to Lee Vining.
Yosemite to SF is about 4.5 hours via CA-120 and I-580.
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I really don't think your Saturday is very doable. Physically you could actually drive through each park and then to SLC, but I can't see you having any time to see anything beyond your car window. Arches and Canyonlands are tough enough to do in one day, I really wouldn't try to add on the drive to SLC on top of that.
I'll also suggest that you even think about how important your detour to SLC is. It adds nearly 300 miles of driving, and then takes you away from a very scenic drive from Moab to Bryce via Capitol Reef. If you are going to keep SLC, then that's where I'd use your extra day. Spend another night in Moab, drive to SLC sunday and spend the night. Head to Bryce monday morning, see the park and spend the night, and then spend Tuesday driving to Grand Canyon via Zion.
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There is a very scenic route that goes from outside Chicago to San Francisco. It passes several off the beaten path National Parks. and for the most part is off the interstate but is close enough to it if weather goes bad.
Try the Lincoln highway-even the Park Service has written that it is a great route if you are not in a hurry.
