Running your own keys is very good advice, but after that the best tricks I use are to try and apply to groups where I would be a good fit, and to make sure that I’m applying to things which are appropriate.
So, on my Outlaw rogue I’m not applying to keys where they already have 2 DPS without lust. That’s going to force them to find a healer that can provide it, which at minimum means I’ll be signed up and waiting until they find a healer first, and more likely means that I’m just not going to get picked. They will probably take the first comparable lust DPS that signs up. I’m also not trying to jump key levels or even sign up for a 13 of a dungeon I’ve timed a 12 in if all my other keys are only at 10-11.
The less concrete advice I have is to put something amusing in your note. I’m not going to take the time to verify that you are a 3k alt, but if you put something in your note that vibes with me that’s going to shift my thinking from why I would take you over an applicant that is you but better, to why I wouldn’t take you. If the vibes are good and you don’t have any red flags then you’re in. I’ve had this work for me more and it’s not super common, so it makes the advice all the more valuable as you will stand out more.
A final thing I do is to just make sure I’m cycling my applications. Unless there’s only a few keys that fit what I need I’m cancelling after being applied for one minute and applying to something new. You can always reapply if needed. You’re going to be more-or-less stuck babysitting your applications anyhow, so you might as well go all out with it.
But seriously you are missing out big time if you aren’t curating your own key at all. It is such a useful way to smooth out rough patches.