LOL feel your pain you are in exactly the same position I'm in.
I say bleed, cos the symptoms and events leading up to failure seem to point to air in the system.
I still can't find a steep ramp to sit on and do the bleed. Might go to my local multi-storey car park this evening and use the ramps that go from floor to floor. They're quite steep. Tried tilting side to side but no improvement.
I'm starting to come to terms that I'm gonna have to remove the dash etc to inspect the damn heater box/matrix/flaps if it doesn't work.
Sh!tty beemers - I was giving it beans on the motorway and the small plastic bit that covers the join btwn windscreen wiper & arm just flew off. Such poor design quality this stuff never happened with my Lexus.