i'm not a jazzmaster expert - but i love the guitar and have looked into the various options.
except for the colour, the classic player is the obvious choice. but colour is important, as we all know. that MIM poly finish is unfortunate. i'm pimping a MIM 70s classic strat at the moment - an excellently put together guitar - but the poly is a bit of a let down - but only because the rest is so good.
apparently there is stuff you can do to a jazzmaster with original bridge to fix it - basically you change the bridge, or do something to give it more tension:
* going for really heavy strings (ie - heavier than 11s) does help alot.
* you can also bodge a tune-a-matic or mustang bridge into the cups of the original intonation piece. it can be done without too much work using tape around the posts. if you want to fit it properly you have to remove the cups, fill the holes, and fit the bridge properly.
* fit a buzz stop to the tremolo:
http://www.northcoastmusic.com/buzzstop/i would try the buzz-stop first if it were me. personally though, this all sounded like a bit of an effort, so i decided to put together my own jazzmaster from parts - work in progress at the moment - hopefully should have it ready around christmas time.