Good post.
My opinion is that you were sort of screwed from the beginning - this really wasn't a BLS transport. Old guy, SOB like that, he could have been in the midst of heart failure, and he really needed ALS care from the outset. (I'm guessing that your boss may have frowned on you calling for ALS support for a call like this, and it's up to you to decide what you want to do about that).
When his respirations became inadequate during transport, you supported them successfully. Other than calling for ALS intercept or preparing for CPR, there isn't much more you can do at a BLS level. I would have told my driver to light up and go at that point, too - once you are bagging somebody, you have every right to hurry to the ER.
I've learned not to expect much from nursing home staff. Sometimes they can be quite good, but they often make poor patient care decisions. You are probably correct when you say you should be more assertive, but it's hard to be assertive when you are new to the job and unsure what to do, especially when your opinion differs from that of more experienced people.
The really important thing was noticing the life threat as it developed, and correctly addressing it.
I think you did all right, considering your situation, and I applaud your effort to learn as much from this experience as you can. That's the right way to get good at this job.