I went from South Rim to Bryce back down to Zion with a 35' FW and had no problems at all. They never gave my rig a first look about going through the tunnel. The worst part of the road was west of the Zion tunnel to the entrance. It was very curvy in a few spots for about 2 miles, but just required hugging the yellow line to keep the trailer on the road as it isn't extremely narrow, just narrow. A 22' trailer wouldn't be a problem at all.
If you are in the area and can spare two nights, suggest adding Bryce to your trip since you are so close. You could do it in a very long day run up from Zion if you would like, but then you would miss out on a sunrise or sunset which is very nice.
2015 Ram 3500 4x4 Crew Cab SRW 6.4 Hemi LB 3.73 (12.4 hand calc avg mpg after 92,000 miles with camper)
2004 Lance 815 (prev: 2004 FW 35'; 1994 TT 30'; Tents)