LC Payback
Its funny you asked, i have been thinking various scenarios myself and here is my train of thougt
It might not appeal to everyone out there!!
Problem is if you want to quit and follow the process, like informing your boss that you are quitting (and possibly looking for a counter offer in case you are disgusted with salary you are making in addition to the gc wait)
Use all your vacation and disappear on the first job offer you get with out telling a soul. best time to do this is right after you get your bonus in march(which i doubt if sprint pays next year)
Most of the managers at sprint don't know great deal about GCs and i don't think Sprint's HR will be chasing you down for the money. If they do, and turn it over to a collection agency, you can negotiate with agency to pay only half the amount, or can get into an agreement to pay $10/month which i doubt if sprint will ever go through that route.
As far as the experience letter, You can get a letter from a co-worker (who can be trusted buddy of yours and happens to work at sprint) in-lieu of an experience letter. I am telling this from my personal experience and was actually suggested by Sprint's appointed lawyer for my LC filing@sprint when my prev employer declined my request for an employment letter. You don't need to pay no stinking $3000 dollars to sprint for experience letter.
Your 401k contributions if any exist might make things complex, as you need to figure out a way to roll that over into another plan like rollover IRA