There's the MILPERSMAN for it. SRT isn't done through CMS-ID/MNA so it's all packages and interviews, your detailer isn't really involved. You'll actually get swapped from your normal IS detailer to a special duty detailer who is pretty hands off until they get word you're accepted (in which case they cut you orders) or you're denied (in which case you're returned to the IS detailer). It would be extremely tough to get orders there right out of A-school. [email protected] is their email address.. could hit them up and see if there are any specific NECs they look for from an IS and try to get that NEC in-route to your first command. At least you'd potentially be doing the kind of work they're going to expect you to have the skills for. There's other NSW billets available that you can apply directly for in MNA (organic SEAL team, group, SBT, EOD, etc) that would get your foot in the door and since most of the SOs know each other if you do good at one of those and show interest in SRT they can talk to the chain over there.
It's highly unlikely they'll pull a fresh A-schooler though. Even if you seem super motivated and have great PRT scores they don't know anything about you. Sure you pass the no DUIs in the last 3 years but you've only been in for one. You have no history showing that you can maintain a certain level of maturity by not going to NJP. While a lot of what you do at places like that is going to be "new" for any rating, they expect you have the capacity to learn it and most of it builds off of concepts you should already know in your job. It's hard to judge how well you'll adapt to learning that kind of stuff if you haven't done anything.