The plan is:
6th-11th Oct - Las Vegas for a stag-do, (hopefully wont involve any tigers, or Mike Tyson's)
11th-17th - National Parks time (11th+17th will be driving days)
18th-20th - Las Vegas again
You can be in Zion National Park in about 2.5-3 hours from Downtown Lost Wages, err I mean Las Vegas.
Page and Bryce are about 1.5-2 hours from Zion's east entrance (albeit in opposite directions).
While ambitious, it would not be unfeasible to do the following.
11th Las Vegas to Springdale, UT (Zion, NP) (3 hours drive time from Las Vegas to Zion)
12th Ruby's Inn (Bryce Canyon) (2 hours drive time from Zion to Bryce)
13th Torrey, UT (Capitol Reef) (3 hours drive time from Bryce to Torrey, and it's a wonderful 3 hours. If you do this, Calf Creek falls
is a MUST stop.)
14th Moab, UT (Canyonlands, NP or Arches, NP (For first timers, I'd say arches)) (3.5 hour drive time from Torrey to Moab)
15th Kyenta, AZ, Bluff or Mexican Hat, UT (Monument Valley) (3 hours from Moab to Monument Valley, 30 more mins to Kyenta)
16th-17th Page, Az (Grand Canyon and antelope). (90 mins from Kyenta to Page, 4.5-5.5 hours from Page to Las Vegas)
Or you could power all the way to Bryce on the first day, and add Springdale/Zion, NP on the last day of the circle.
There would be some long days but you'd see ALOT of the SW US....
If you need any help route finding (which highways to take, PM or email me.)