something to consider is that thieves aren't stupid most of the time. 90% of people do what you are doing right this minute, replacing the stereo with a new one. Time and time again when this happens the new stereo is stolen again because the thieves watch the car for the new system to go in.
talk to your insurance company and just get the money. If you have proof of what was in there before and that is was stolen, then tell them you only want a check for $1000. They have no right to tell you to go to a certain shop or how to spend your own hard earned money, you pay them a monthly fee to get your money back in a case like this, not to let them also get a kickback from shops because they send a ton of business there. Flat out what they are doing is illegal, and you should tell them so (report to the BBB if you have to).
take your check and hold on to it (or spend it on something else). Maybe get a new HU and always take the faceplate, but dont install anyting else until at least a few months have passed and then consider a replacement for the rest of the equpiment.
btw, this happened to my friend last year. We got his receipts and photos of when we installed it all to provide the insurance company. A month or so later he got the approval and a check in the mail for the full amout he paid. That is how insurance works, not requiring you to get new equipment and installation and a perticular shop. Hell, even in body repair for accidents they can't require you to get it dont at a shop, they can only require perticular shops for a quote.