Agree regarding buy back and repair comments - it happens far more often than you'd think.
The problem is insurance companies will only use new and genuine parts and their preferred paint / body shops etc which will have a nice expensive deal going with the insurance companies.
I know you say you've got a 20v so will be a newer / facelift 156 but if you think about all the older non-facelift vehicles out there a brand new door from Alfa is probably more than you'd pay for the entire car.
Just make sure if you do buy it back you give it a proper inspection first, particularly mechanically if you're NSR wheel has taken a thump. Just to make sure that you're not getting yourself into any dramas with rear sub-frames and suspension arms / legs being bent up. That way you have an honest opinion and assessment of what needs to be done to put the car back to how you want it and you can work out whether that's financially or practically viable for you.
Don't let the insurance company give you a bum value either - you can almost guarantee the first value will be a low ball effort. Have a scout on the classifieds, ebay, autotrader, pistonheads etc etc and find some values (preferably garage forecourt - they're valued higher) and provide examples of vehicles the same age / milage / history as yours and argue with them.
lastly, good luck. I've got my fingers crossed for you.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso