There are pros and cons to what you are describing.
My credentials are similar to what you describe, but for different reasons. My original degree is a BA in biology. When I decided to become a nurse, I went back for a associate degree.
I had no problem getting into anesthesia school, although that was a while ago. You seem well versed in the issue of acceptable degrees for various programs, so no need to go into that.
I believe that you are right about the value of a strong science background. I believe my previous biology/chemistry/physics courses gave me an edge in these classes in anesthesia school. I still find instances in my anesthesia practice where my science background is a benefit to me.
On the other hand, professional nursing treats us non-BSN nurses with very little respect. How much that matters to you, depends on your future plans. It is quite possible to become a CRNA, go on your merry way, and not give a hoot about what "they" think of you.
Not having a BSN has limited my opportunities in some ways. Masters programs did not want to admit me until I earned a BSN first. A nursing masters is required for APN status in my state (but CRNAs do not have to meet this requirement to practice anesthesia). Lack of a BSN may be a barrier to getting a job in education, or being appointed to a Board of Nursing.
Granted, I think in the big picture these are probably not priorities to you right now. And if they ever get to be issues for you in the future, you will just have to find ways around them, as I have done.
So over all, I think you have a good plan. Just thought I would share what I have experienced, so you can see the whole picture.