Another $.02
As others have said above, the trouble with flushing a system to try to eliminate any metal filings/particles is that there is no way to really guarantee that you got ALL of them out. Sure you can flush the lines without much trouble, but its in the exchangers (the 2 condensers and the evaporator) where its just about impossible to get everything out.
If this were my problem, and I didn't have the coin to replace the exchangers along with the compressor, expansion valve, and the receiver/dryer. I would tear EVERYTHING down and flush everything as best as possible. Install the new compressor, expansion valve, and the receiver/dryer. If any particles were not flushed out they will hopefully be small enough to not cause damage to the new compressor, and will be caught by the new receiver/dryer (which is designed to trap particles and any water vapor that has got into the system).
The problem taking this approach is that unless you are doing the work yourself (as I do), it may cost you almost as much in labor to pull apart everything and flush the parts, as it would to just buy all the new parts. You will have to check it out.
The other option is to just do the quick (non-disassembly) system flush (as I am sure your cheaper estimate guys are planning to do), put the new parts in, vacuum pump and refill the system, and hope for the best. Perhaps there weren't any real metal filings in the system after all, because unless those guys who gave you the $4k estimate flushed the system and saw filings, then they are just theorizing, and covering their butts.