Yes! It worked! I learned something by getting embarrassed online!!!

ike, you're absolutely correct. I applied conservation of expected evidence to likelihood ratios instead of to posterior probabilities, and thus didn't realize that the prior puts bounds on expected likelihood ratios. This also means that the numbers I suggested (1% of 1:2000, 99% of 20:1) define the prior precisely at 98.997%.

I'm going to leave the fight to defend the reputation of Bayesian inference to you and go do some math exercises.