The old 16.5 was the first generation of a solid rim, replacing the old widow making split rims. Good ridance split rims and tubes. The tire/rim engineers retained the shallow bead when producing these 'new' tires/rims. It is NOT a modern safety bead tire and when they get low or go flat, they will have a tendency to come off the rim. (Ask me, I know.
) You'll easily see the differnce with 16.5 beads next to a modern safety bead type. 16.5's are not dangerous or unsafe, there is simply a better safety alternative in the newer 16 and 17 inch safety bead tires/rims. This should be a consideration with a top heavy vehicle like an RV. BTW, if you're current tires are dry rotted, they are simply d-o-n-e.
The 16.5inch tires are still out there, but getting rarer by the day. And if you do find them, they may have some years on them from just sitting on the shelf(think dry rot and shorter calendar life). Domestic manufacturers will stop producing them due to light volume and source them off shore to save the headache of setting up lines for short runs. So quality will likely take a dive. Eventually, if not already, the cost of aquiring E rated 16.5 tires will exceed the cost of converting to 16 or 17 rims. I still run the 16.5's on one of my old trucks, but as soon as they are all worn out, I'll switch to 16's or 17's depending on price and availability at that time. Sure it would be expensive to convert to the newer size tire AND rim, but think about having to come up with an unpopular tire size during travel in lightly populated areas?
If you do stick with the 16.5's keep your old tires for spares or at least pick out the best two or three if storage is an issue. Likewise, if you do convert to 16 or 17, you could mitigate cost by buying a used tire for a spare. Do stick with the E rating or at least D. C ratings (6ply) just won't cut it for a Class C motorhome.
When we travel more than a day from home, I carry TWO spares. I've yet to use two, but have used one about every other year. And when I've had flats they've generally been in desolate areas. I've got good quality tires, they just take a beating on gravel and industrial roads when not pulling the TT. If you don't have a second spare rim, just carry a spare tire and upon changing a flat, make a beeline to a tire shop and have #2 spare mounted and the old one patched...It's also lighter to just carry the second spare tire sans rim.
Used rims can be had for ~$50 a pop. Just be sure they are not bent and run true. Take your spare or your worst tire/rim and dismount the tire. Take the rim to the salvage yard and ask for an exact match on bolt circle, pilot diameter and offset but in the 16 or 17 inch version. The sizes are stamped on the inside of the rim. If you're buying 7 or 8 rims, ask for a package deal and offer to trade in your old ones. You can mount the bare rim on the front and rotate it by hand to check runout. If in doubt, you can always buy new, but those will be $100 to $150 a pop. For a used vehicle that may not see many miles, that's pretty expensive. I'd rather buy used rims and put the balance of $$ in quality tires and the gas tank and DRIVE!
Do a little homework and price the size on your truck in the 16.5, 16 and 17. As an example of a size, 235/85x16E is extremely common and the newer 17inch version is 235/80x17E. If it were me and I was forced to convert, I would go to the 17's (assuming $ competitive) as the 16's will go the way of the 16.5's at some point in the future.(it'll be a while) All the Dually's made now(and for the last several years) use the 17inch rim. This was done to accomodate slightly larger brakes on the new trucks.
Good luck, be safe.