Mixing radial and bias ply tires on the same axle is a no-no. As long as both sides of the axle have the same type of tire, you're probably OK.

I've got an old Dodge 1-ton chassis 24-foot Banner motorhome with bias ply tube type tires all around, and it will rattle my teeth for the first 20 miles after it's been sitting unused for a few days. If the ply material is nylon, that's definitely your problem. We used to call it "nylon thump" 40 years ago. As the tire warms up and gets flexible, the flat spots will go away and the ride will improve. It gets worse in cold weather.

16.5's were designed to have the same overall height as tube-type 15" tires, but I'm not sure how the sizes interchange. We used to use 11-22.5's on the same hub as 10.00-20's, with no tire height problems, IIRC.
Jerry

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