I think your biggest weakness is right here:
"Applying to job opportunities en masse (30-50 applications/day with my default, non-customized resume)"
Shotgunning the same resume and cover letter to jobs rarely works when you're first starting out because you don't have a wide range of experience to draw from to make universally appealing stories. Instead, you have to make experience A relevant for a job that is looking for experience B. This is hard to do since each job is looking for something unique.
I would reduce the number of jobs you're applying to per day and write unique cover letters for each, and if you can, maybe even a unique resume.
"Is a referral the deciding factor between two candidates that are equally qualified, equally liked (during interviews), etc?"
Almost always it comes down to the quality of the applicants. It's pretty rare to see a situation where two people are so evenly matched that a referral pushes them over one way or another.
"For a highly competitive opening at a popular company, is the referral the best chance to land the job?"
No. The best way to get the job is to have the skills the job requires and prove that you are the best one for the job. Do not rely on referrals to help you close the job. You can ask them to make an intro, but like the below comment, you need to have the goods once the intro is made.
I would do the following:
Find recruiters for this company and reach out to them expressing your interest for the soon-to-be created role. Attach your resume and make sure your resume is super personalized for the role you want for this specific company and see if any respond back to you.
Here's a starting template:
“Hi - I’ve been a huge fan of for years, and though I’ve been a at for X years now, I’ve been keeping my eye out for opportunities at . I saw that you are hiring for a and that you’re building out a new team for . It seems my skill set might be valuable to this new team and if you're looking for I would love to chat with you over a cup of coffee."
Best of luck!
My advice would be to use the analytics channels at your disposal and try and figure out any trends. Highly recommend you sharpen your excel/Google Sheets skills so that you can pull data and manipulate it to find trends.
For example, if you’re trying to grow engagement on Twitter or Instagram, see if you can figure out what hashtags drive the most engagement. Also, take advantage of trending hashtags relevant to you based on your business vertical (e.g. #FlashbackFriday, #WednesdayWisdom, etc.).
Biggest piece of advice I can though is to post often and track all the variables of your post (e.g. Time of post, day of post, content, text-only, image, album, etc.) Your challenge is to find that one thing that takes off.
+1! Getting creative with your resume is definitely a way to stand out.