I‘m going to list RV parks I have experience with. First choice would be trailer village. Given the size of your rig the access to the sites will be MUCH easier. Full hook ups a plus.
https://www.visitgrandcanyon.com/tr...edium=local&utm_campaign=trailervillagervpark
Check the NPS site for camping/RV info. You will see Mather Campground listed. No hook ups and the roads accessing some sites can be a real challenge with larger rigs. I’m not familiar with all areas of the campground but the area I’ve stayed in frequently has a couple of real tight areas on the acccess roads.
https://www.nps.gov/grca/planyourvisit/camping.htm
There are two KOAs near the junction of I40 and 64. Both are OK? but are approx 45 and 50 miles from the south rim entrance. One KOA is just off I 40 near Williams and the other is off 64 a bit closer to the canyon. I would pick the I 40 campground.
If you’d like to know my #1 reason, PM me.
These are four I have experience with. I believe there is another short term park in Tusayan that I have no personal experience with.
Keep a watch on the NPS web site for current closure of south rim attractions. For example the east entrance to the south rim was closed much of last season for Covid reasons. (That route passes thru the Rez)
Also contact at least trailer village ASAP as they fill up fast.
What route do you plan to take from Moab to south rim ?