While there's a lot of PM roles available now, there's also a lot of candidates applying. How would you suggest optimizing your resume or application process to stand out and get an interview?

I'll be blunt: because of the huge number of PMs on the market right now, you need to either have or find a connection into the company where you want to work. Simply optimizing your resume or cover letter isn't going to cut it; nothing beats a personal referral, or a warm intro, even if it is a few steps removed. Figure out how to use your LinkedIn 2nd or 3rd degree connections to get you to someone who's even proximate to the hiring manager for the position, and you will be miles ahead.