The only suggestion I can make to you is to try to get into a hospital working as an anesthesia assistant (might be called by another name in different hospitals). AA's usually are students who work in the OR and turn over the anesthesia machines between cases. They also run for things anesthesia needs during cases, and they also run for the OR nurses, (it's a lot of "running"). All our AA's are mostly students (nursing, physician assistant,pre-med, lapsed students, etc.) This would let you in the OR and allow you to work with both CRNA's and anesthesia doctors (remember as a CRNA you work under the guidance of the anesthesia doctor at all times). Sometimes the AA's hover around in the OR and just watch things. At least this is how it works in my teaching hospital. But mostly you are running your butt off and taking a lot of flak from the various people in the OR.
I think you are deciding too soon as your post implies. I understand your need to get somewhere as quickly as possible. You obviously need your RN and to work some before you can really see the big picture. I've read your other posts and I think either way you go, BSN or MSN, is going to take some time. Becoming an OR nurse will not help you get into CRNA school because the schools don't consider OR nurses as critical care nurses in the same respect as they do ICU nurses, and I believe that is a correct observation. So in my opinion only, the only way to many higher RN's designations is via ICU because the patient care is the most acute and intense.
CRNA is probably the most acute care position in nursing in my opinion. The patient is literally in your hands, unconscous and usually paralyzed and you are physically keeping them alive with multiple drugs while someone is working inside their body. It's not for everyone, it's literally for only the very very few. And be aware, anesthesia is blamed for everything in the OR, from turn over time, to the flinch of a patient's finger during the surgery. It can be very intimidating having surgeons screaming at you, or patients coding while open on the table. That's why you need to see it, I don't see how you could possibly be informed of that aspect of the job from working in the ICU.
No matter what route you take with your education you are going to have to pay your dues with plain old bedside care before you can do much else. It separates the "men from the boys" so to speak. CRNA schools are a lot more competitive than what you are experiencing just trying to get into ADN, BSN, and (vanilla) MSN programs. If the BSN and MSN programs take the same amount of time, you're still going to have to be "just a nurse" for a while. I could be wrong but I sense you don't really want to do anything bedside in a hospital, you are seeing things only as a white coat-clip board sort of nursing ideal. That's common for all of us (me too) dreaming of that perfect nursing position. I'm really not trying to discourage you, although it reads that way in re-reading what I have written. I'm just trying to make you see that you just don't go to school and suddenly you are a nurse, any kind of nurse. You really know next to nothing after getting out of school other than the ideals that are taught, which don't exist in the real world. Being a new MSN graduate, you are no more prepared to put your hands on a patient and take care of them than any other nurse fresh out of school.
Everyone can carve out their own niche and get where they want to go with enough desire and drive. Everyone's route to getting there is different. I don't think anyone here can do much but give you opinions. It really just depends on you.