If I understand your question, you want to know if you can bike commute 45 minutes each way in zone 1, AND do your training program described in your post (as opposed to training DURING your commute).

You can. I have a similiar commute in terms in length, and bike commuted while training for Ironman. The Zone 1 commuting will be good recovery, but please let us know how you're fairing after the first month (I have no comment with regards to the actual structure of your training plan).

You are talking about 7.5 hours of commuting plus 10.5 to 12 hours of training. That seems like a lot to me. One of the beauties of bike commuting is you can reduce a little bit of your training time (particularly zone 1 and zone 2 recovery rides).