OK - That quote doesn't seem too bad given the value of the car. In the past I have been offered another option by my insurers - usually when an engineer comes to asses the damage, they can agree a settlement with you for you to get the repairs sorted yourself.
The insurance company should always pursue the costs (including your excess) from the third party - especially as they crashed into your parked vehicle. I don't think it matters whether your car is on private property or not - as long as you were not doing anything that would exclude you from being insured (like a track day) there should be no problem... when you first insure your car they always ask where it is parked during the day and at night, so if it was parked in one of those spots there should definitely be no problem...
I would spend some time on the phone with your insurers (ask to speak to managers etc.) explaining that the reason you purchased this car was for the value of rarity, and if you can prove with receipts and your history that the car has always had BMW parts and or been serviced only by BMW then they should be able to agree to have the car fixed if not by BMW then by a BMW approved repair shop. You might even find that a BMW approved place is one of the insurers approved too
I had exactly the same experience as you about 10 years ago with a VW Golf GTI - it took me a month to convince my insurer to pay for a VW approved repair shop at about 4K - the same cost as you have been quoted by BMW...
Good Luck - I hope you can get this sorted!