WHAT??? Now that's jacked up ..... Have you had any type of negative light at your command?? I hate to say it but that may be a show stopper for you my friend.... They say that the Skipper's endorsement is the single most important document in the entire package .....
Are you actually an IT or is that just your username for the hell of it??? If you are an IT, that gives you a bit of a leg up on me .. It seems that ITs are the primary selectees for the SWO(IP) program .... its funny how an AS got an alternate spot huh?? You don't even know how many ITs looked me up in the global last year and were like " what did you have in your package that helped you get selected" lol .... I am only about 4 classes away from completing my CS degree .... hope that overtakes my lack of experience in the IT field.
Have you discussed with your CO at all. It seems that if he didn't recommend you... for whatever reason, he would at last talk to you about it. Could be that having just made E-5 and put into a leadership role, he feels that you are too short on supervisory experience (which I take issue with, as you will gain much experience as a leader as an O-1/2 in the fleet...). "That's what Chiefs are for"! I would discuss with the XO to get an assessment on how to find out the reason for the non-rec, and what you can do toward eliminating any perceived shortcomings.
In the meantime, I would go ahead and submit the package... realizing that if you don't, there is NO chance. Ya' just never know!
The more I think about your situation, the more puzzled I am. You state your CO didn't endorse you (or the other applicant)... did you mean none at all, or no positive endorsement? Unless things have changed, the CO endorsement is required on an applicant package, be it positive, lukewarm, or negative in the CO's opinion. When negative, normally deficient area(s) would be mentioned in the endorsent, and discussed with the applicant.
How did you determine the other 'guy' was more qualified... in what areas? Did he show you his package? I sure wouldn't give up on your application just yet!
I am probably going to apply to about 6 or so schools... Possibly more. Texas A&M, Rice University, University of Florida, Old Dominion University, Arizona State University, and a few more. Once you get admitted to the school, you will need to have all of your transfer credits evaluated. The academic advisors will then create a degree plan showing that you can graduate in the time required by your program option.