As far as using Fargorate for the 3 picks, I think it could work well. The only reservation I have is for players who (intentionally or not) babysit their rating.
I think for purposes of picking the Mosconi Cup team if they ran Fargorate with an algorithm that only used results from the past three years and where it weighted the three years somewhere along these lines it would probably work real good:
Past year counts 55%
Year before that counts 30%
Year before that counts 15%
I could even see running with just two years history and weighted 60/40 or possibly 65/35 just for the purposes of picking the team. Babysitting the rating is a tougher issue to solve. You could have a requirement that a certain number of major tournaments had to be played, like say five, and this would pretty much eliminate the babysitting problem. But then you have the problem of one of your best maybe not playing the required amount of majors for whatever reason. Like if Shane chose to only play in three majors for the year he is still clearly the best player but he wouldn't be meeting the criteria and you sure wouldn't want to have to leave him out.
Maybe your suggestion where they use Fargorate only for the top 3 and then have 2 still be captain's picks is the best all around solution if used in conjunction with a minimum number of majors criteria in order to be considered for the top 3 per Fargorate. That way if somebody who is clearly playing great didn't play the minimum required number of majors they can still be selected as one of the captain's picks.