That’s a good idea with the rim only-thanks. I’m asking the seller to do it, but they aren’t local to me-hope I can trust them.With that many weights I'd say either bad wheel or bad tire, or both.
I had similar problem with one on my tt tires.
I made tire seller spin my rim, found to be good. They couldn't balance with tire without a ton of weights in any position.
Hence bad tire. They installed another tire and all went well.
You should never need excessive weight to balance a tire.
Paul B