OP, If you want to go to the research and shopping, you CAN find 16" wheels that will work. You may even find some with serviceable tires on them. Depends on how long Chevy/GMC stayed with 16's that have characteristics equivalent to your 16.5's. I think OP in the Lengthy Tread linked above, decided all that wasn't worth the trouble and sounded ready to stay with 16.5.
Do NOT Stock Up! Even with travel like you plan, most of us will not wear RV tires out. They will AGE Out first. There's DOT coding molded into tire sidewalls. One only one sidewall, there's a four-digit production date branded on the end of that coding string. WWYY, where WW is Week Produced and YY is Year Produced, so 0517 would be the fifth week (sometime around FEB) of this year. Always ask for, make that Insist On, Recent Production Dates.
Tires age out even unused. Dodge Van, single rear wheels, 800/16.5 tires. Came with five beautiful Goodyears that ran great for years. As they were wearing out, I found an unused one at Firestone. Mounted it with my identical unused spare and two new tires.
First, I did not get Half the Mileage on those New/Old tires that I did when the set was new.
Second, I bought "take-off" tires for the other two. On CARS, they might come off because of the Look - Owner wants something with/without white letters, etc. On a Commercial tire, they probably come off because they were so out of round or out of balance the driver couldn't hold onto the steering wheel. At least that was what I found.
I replaced them all with a set of 875R16.5 and the change was wonderful! Never looked back.
Please find your door jamb label and reply with what it says about Tire Size, Type (hopefully Load Range or "Ply") and Axle Ratings for Front and Rear.
The 800 size is gone. What tire companies did was go to 875, which almost always replaces 800 without problems. They also quit offering Load Ranges C and D and offer only 875R16.5E.
In the Lengthy Thread, Capri Racer (barrystiretech in another site I linked) said the 875 should work with rims originally used for 800. Another OP was concerned about E tires rated at 80 PSI and the old rims are probably not. Your axle weights are not going to require more than the 65 that D tires could go to. Another mentioned that radials use a different bead area of the rim than old bias tires did. I personally never heard that, and I know I had no problems with radial on my truck that had been built in 1971 with bias tires.