Auto Owners Insurance Low Ball offer on Collector Car, proof of my claim in plain sight Lansing, Michigan

Well first don't call a 2001 Audi a "Collector Car".  Yes it may be a very nice car, and yes you may have kept meticulous care of it.  But when people hear "collector car" they think of cars pre 70's/80's worth in the high 5 digits to 6 digits.  Not a relativity new(only 12 years old) car.  But that's just a suggestion..take it for what you want.

Also, not sure where you are getting your $10,600 Blue Book value.  Went to kbb and put in the criteria you mentioned.  Private Party price is only $6,790 in Excellent Condition(which kbb states only 3% of the vehicles fall into).  Even the Dealer Retail is listed at only $8,715.  This was with pretty much every option listed, so not sure how you are getting the extra almost $2,000 above that price.

Keep in mind that people can "ask" for any price they want.  After all you could ask 1.5 Million for the car..it is up to someone if they want to actually pay that. 

But with all of this said if you don't like the price you are being offered, you can fight with the insurance company with your proof.  Or you can file suit against the driver/insurance company.  Depending on your state you are most likely above the Small Claims limit.  Some states have a $10,000 limit so in this case it may be to your advantage to just forget about $600 and sue them for the limit so you can keep it in small claims. 

If you can't keep it in small claims you may need to deal with lawyers, but if you can show that your car is worth more than they are offering and convince a judge of that, you would not only most likely prevail, but the other party would be responsible for your court costs as well.  Just be careful because if you settle for the almost 7,000 thinking you can fight for the difference later. If they have you sign anything, you would also most likely bar yourself from any future claims.