How to deal with LFBGA217 package when building prototype boards by hand
From my experience, one-off assembly is extremely expensive in the US. Most places would not even bother giving me a quote for a single piece. Furthermore, you're likely to have the same problem with building a breakout board, since that will have to be assembled (it just displaces the problem). However, I have found that (with some work), it is possible to do BGA parts if you have access to a reflow oven, or if you have access to a fairly good heat-gun. 

For heat gun instructions: http://devbisme.webfactional.com/blogs/devbisme/2012/08/24/mounting-bga-pcb-quickly-and-cheaply

For a reflow oven:
I used #186 rosin flux at 295 C for 90 seconds with a 200 C preheat (180 seconds). This is higher than most manufacturers recommend, but the oven I have access to was donated to the University and is from the early 90s, so it doesn't actually get that hot. It was not necessary for me to use a stencil or even apply any solder paste, I simply coated the footprint area with flux and carefully aligned the package to the silkscreen.

One bit of layout advice if you do not have access to an oven is to make the board as small as possible. This makes it possible to heat up the entire board to a consistent temperature.

Also remember to tent vias under the BGA, if you do not, capillary action will cause the solder to flow from the balls into the vias, which is not what you want to do. http://siliconexposed.blogspot.com/2012/07/bga-process-notes.html

Finally, if you don't have access to x-ray inspection, make sure your silkscreen outline is precise. It should be slightly bigger than the package to assist you in aligning the part. You can print out the silkscreen layer in Eagle on a conventional laser printer with 1:1 scale to make sure you can align it on paper first.