Hello Jim, thanks for reminding me about the AC drain, as that is the critical area of heater matrix removal without draining down the AC.
As for the mechanic doing the matrix change in record time, as far as I am aware, he manages to do it without complete removal of the dash. I have not seen his work but suspect there is a lot of bending and brute force involved. Maybe he does not refit the dash, going for that lightweight look.
The plastic elbows!

I always strip out cold, as I take the view, if they are brittle through age hardening and cavitation, they deserve to break! They can be replaced by getting another set from the breakers yard. It is easy to remove the hoses, as the bonding can be detached, just leaving the elbows to be removed and replaced, using jubilee clips to hold the hoses onto the replacement elbows.
Handyman