Nope, everyone seems to be vetted through the same application process (obviously little things might be different depending on your trade, like needing to score such and such on your eye test in the medical for X trade). My brother and I are getting in near the same time purely because we applied near the same time - also he went Navy.
You know what does really help the application process - scoring well on the CFAT! Might not speed up the process directly, but its truly the best way to beat out others on the competition list once you get there. Not to diminish the interview or anything, but man does the CFAT get brought up a lot. The CFAT truly was the best thing I had going for me, I am a high school drop out but because I studied I still scored really well and ended up being very competitive for my trade.
The whole process from applying to going to BMQ seems to be fairly long for almost everyone, so use that time to your advantage and study up on your trade. If you score well on the CFAT, pass the medical, and do well in the interview - your going to be golden. I had been in the process for about a year by the time I did my interview and it ended up being the most enjoyable and easy interview I've ever had! I knew what I was signing up for, seemed capable to be able to learn it, and I was highly motivated.
The only way to possibly speed up the process is to answer your phone/emails asap, and always try to get whatever documentation they ask you for to them asap. Be proactive, which seems to be natural for you!