What are some things I can do in order to distinguish myself for a waiver from E-3 to E-4?

When that list comes out in PSG meetings with the 1SG lots of things are brought up, especially when limited waivers are available and multiple people are being considered. Biggest things I advocate for are PT, day to day performance, and initiative. Act like the rank you want to be. Take responsibility when guidance isn’t given. Don’t sit around in the bay when not being told what to do directly. Motivate those around you with a positive attitude when things are less than ideal.

Strive to improve at what you do in the Army. Understand you won't be perfect but be better than everyone else around you. Take care of the soldiers around you, but not to the point where it starts to become a burden on you, you have to be squared away before you can square others away. If you're in charge of a detail, or a group of soldiers be open to input from others, find the best way to accomplish your task as long as it doesn't involve cutting corners. Teach the new soldiers that are lower ranking. Start learning the creed of the non commissioned officer and learning regulations. Take initiative, if you know something needs to be done then grab some guys and get it done. And most important, do the right thing!

In seeing that you posted about failing height/weight on a diagnostic APFT, that's something I would get in order. Even though it seems small, button up that hatch to where a commander can't say that you have something you're not taking care of.

One word. Initiative. No one will take your career as seriously as you do. That being said, take initiative to strengthen your body so you score higher on your Apft. Strengthen your mind by completing professional military education as well as civilian education. Exhibit a positive attitude and strive to the best you each day. Always maintain a squared away appearance and always be punctual. These traits won't go unnoticed.

I lost a waiver for one of my guys to another platoon because the other guy had one more point on his last APFT than my guy.

Get SSD1 done, or whatever they are changing it too.