Of course you can flush an AC system. Read the service manual! My vacuum pump cost $100. Where did you get a figure of $1600?

Evaporator and condenser coils and the various lines can be flushed. The O-tube, mufflers, and the compressor should NOT be flushed. Condensers are best replaced if the system had a compressor explode.

Laquer thinner makes a decent flush agent. It's cheap and readily available. Needs to be shot through the system under some pressure, so a flush bottle is needed. Dry shop air can then be used to expel all the flush agent. Reassemble using new o-rings and the proper oil, then evac the system to boil off any moisture. If no leaks, follow up with a charge of the proper amount of refrigerent.

Steve