If you have the weekend of October 19-20 or 26-27 available, you could do it all on the shuttle for under $1,000, most of it on one of those weekends. Buy tickets soon, because there are some advance purchase limitations on these fares.

LGA-DCA-LGA-BOS-LGA for about $231 (on Orbitz) on Saturday, starting on the first flight out. Do the same thing on Sunday for the same fare. Add a round trip for $116 LGA-DCA-LGA on Saturday evening and you've got 20,000 base miles.

The current triple base miles for shuttle flights (through 12/31) makes each segment worth 1,500 base miles. The ten segments above make 15,000 base miles, all for under $600.

Given how many other weekends there are until the end of the year, I'm sure you can work out the remaining 7,000 miles later on (after the double base miles promotion expires) for another $350 or so.

For more info, see this link:
http://www.flyertalk.com/forum/Forum21/HTML/007367.html

Also, I wouldn't take the risk that the 5K for the Platinum card will post in time to count for this year. Mine took about eight weeks after my first purchase to post.

[Edited to fix a serious glitch, accurately pointed out by Northern Willy below!]

[This message has been edited by Dave M (edited 10-09-2002).]