You will be sorry not making reservations at any of those 3 places and surrounding areas. I was in Zion in June this year. My son and I waited for almost 90 minutes to get on the shuttle at the Zion visitor center at mid day. Ranger said the other stops were not anything like that and they weren't. The last stop we had to wait for a couple shuttles maybe 20 minutes or so but all the others were no problem. Sure wasn't anything like it used to be years ago that's for sure but still worth seeing. Bryce was busy but ok, the shuttle would certainly alleviate any parking concerns. Canyon lands while significantly fewer people it has less parking and camping so it will be busy in that regard. Arches will be busy as well and the campground there is pretty small. Again while not nearly as easy to navigate them as it used to be they are still worth seeing.
Not sure what you are driving but if you have a TV or toad in Capital Reef go down the Notom Rd on the east side of the park take it to the Burr Trail go up the Burr trail and you will come out at Boulder on HWY 12 take 12 down into Torrey and back to your starting place. Take a few hours but the Notom/Burr Trail are fairly lightly traveled and scenery is great. Hopefully you will have already or will be taking hwy 12 towards Bryce/Zion as that is a must drive. In Canyon Lands again if you have TV or decent toad you can take the Schaefer trail from Canyonlands Island in the Sky section down into Moab instead of taking the main road back out, high clearance would be good but no need for 4wd. Don't forget to stop at Dead Horse Point while up there. Also south of Moab near the Needles district of Canyonlands is the Rim Recreation Area good road leading out to the rim in 2 or 3 places road all paved iirc.