Also I encourage you to look into Cryptology... It sounded to me like the cryptos did more of the exciting, deep, intelligence type of work. I have no experience with this whatsoever, but from talking to a couple crypto/intel people, crypto sounded like the most fun to me... Just check it out at least.
Also, the application process CAN be faster that 6-10 months.... A lot of it depends on you. The application process (for any community) is long and tedious, but a huge deciding factor on how long it takes is the applicant himself.
I have a friend that graduated college and applied for a supply slot. She went from talking to the recruiter, to showing up at OCS in less than 3 months.
Granted, anything the recruiter needed, she had gotten him that day... She FLEW through the application stuff. Some things are out of your control... The boards can take a month or two to review your package after it is submitted, again, that stuff is out of your hands... But if you hit the application hard, it will cut down on your waiting time.
Stay away from enlisted recruiters. Many of them are used car salesmen with a rank. They will do/say anything to fill their quota. As far as enlisting with the goal of becoming an officer, definitely counterproductive. This is the toughest, most indirect route you can take if that is your end goal.
You sound qualified and reasonably motivated. If you are sure the NAVY is for you, i'd recommend contacting an officer recruiter, starting the application process, and asking to shadow a few officers for a day (just to make sure it's for you)... Most recruiters are happy to set this up for you, although i'm not sure how that'd work with an intel o, with the sensitive information, etc. This is the best way to get direct answers to your questions.