2004 Acura TSX A/C Compressor Locked

Few months ago my A/C would intermittently stop blowing cold air, I would turn it off and on a few times or play with the buttons and it would eventually start blowing cold air again. This happened a couple times a month but I was never without the A/C for more than a few hours. Last week it stop blowing cold air and has yet to work. I took it to the Acura dealership today and they told me the compressor locked up and shot debris through the whole system and I need to replace every component in the A/C. My Acura is no longer under warranty and I did not buy the extended warranty. They told me it would cost $2,700.00 to replace the whole A/C but Acura would be willing to pay for 75% which means my portion would cost about $800.00 + tax. They said they had to replace all components because if they only replace one the compressor could lock up again and ruin it so I should replace the whole system. Does this sound legitimate? Should I take it to a Honda dealership or other Import shop to see if I can get a cheaper price? This car has very low miles, I only work 2 miles from home but I also live in Tampa, FL and the summers here are unbearable without A/C. Is it worth it to replace the whole system or are they taking advantage of me being a young woman with no knowledge of cars?