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Hello and welcome to the forum.
Your plan should work,and if the bleed nipples are seized/snapped,then you have no other option.
Once you changed the 'stat and topped up the coolant,make sure the heater is on hot and keep the car revving at fast idle speed(2,500 to 3,000 rpm).The coolant should eventually start circulating.Obviously,if the temperature gauge goes above 3/4,then switch it off,leave it cool,top up the coolant again and repeat the excercise.
You can also try and remove the header tank from it's mountings and lift it up higher,this will encourage the air to bleed out of it.
Good luck,and let us know how it goes.
I'd rather push my Alfa than drive a BMW....
Currently in Lagdti's garage:
2004 Saab 9-5 HOT Aero and a 2001 Audi A3 1.8 Turbo