Hi, I don't even consider myself an amateur mathematician, so proposing a resolution to Bertrand's paradox feels to me quite presumptuous.
But I think i really do have a solution. It hinges on the fact that a chord must have both a length and an orientation. And while ranging over either length or orientation, the other property must in a one-to-one correspondence with it. Or they'll be chords without either length or orientation. I also demonstrated exactly how the other 2 solutions differ quantitatively from the correct solution.
It's here at https://miniverse.blogspot.com/2006/12/solution-to-bertrands-paradox.html
I hope that you guys having more expertise than I do can either refute or verify my claim. I sincerely think I have proposed a plausible solution, so hope I didn't waste your time.