Hummingfrog,
TUPE wouldn't apply, as you well know, using the analogy you have. If you had been type qual'd (& a little younger) you would be Bristow, as would the others that were let go with you.
So 'type' would nullify TUPE.
Putting aside TUPE, Mil SAR crews are a must for Bristow & they know it. It's just a case of making it work. That may become the stumbling block.