What can I do to make myself stand out when preparing and submitting my 153A packet?

Does MOS matter? Most of the guys I know that went 153A were grunts, which certainly doesn't give you any experience unless you count hanging your feet out the door of a Blackhawk. As far as I know, your performance on the SIFT, ASVAB score, evaluations in your current MOS and LOR's for any pilots you know go a long way. If you don't know any pilots, I would contact my local aviation unit and arrange to meet some.

If you want to be a WO, talk to one. I don't fly so I am not going to go into that area.
A couple of useful links: https://recruiting.army.mil/ISO/AWOR/153A/
https://recruiting.army.mil/ISO/AWOR/BASIC_QUALIFICATION/
https://usacac.army.mil/organizations/cace/wocc

This should help you get started. Is there an aviation unit near you? If so try to reach out and contact them for more information.

If Fort Rucker is still the school location, go there and poke around (ask questions) pilots and the school without being a pain in the ass.

Sell yourself, two suggestions as far as the packet goes; 1: make sure your LORs are very strong (9/10 times you’re writing them yourself and the endorser will make suggestions off your interviews). 2. Make your resume as strong as your LORs. Not sure exactly how they rack and stack/rate 153A packets as it’s not a direct PMOS transfer. Again, LORs and your resume should be heavily thought out. I was FQ-S on the March board and I personally think my LORs and resume were very well written and had a great impact on getting selected.