Breaking into ER during Off-Cycle

I've been trying to break into ER for the past 2 months following graduation from a target with one summer of IB experience at a small no-name boutique, and several other things on the resume that should convey my interest in the markets (numerous investment books read, investment club activities, etc.).

I've been able to interview at a few places and talk with people from the BBs, but for the most part BBs aren't hiring except for spots that randomly open up when associates leave after a year, two, or three. How do I manage to get interviews with the places I'm networking with people? Do I just need to wait until September when interns have left to maneuver into spots that they would have taken if they got full-time offers?

It doesn't seem like too many people get hired during the summer for FT, but I want to be at the top of the pile to be selected for interviews if spots open up; I also don't want to annoy the analysts I'm talking with because they're busy with earnings season rn. I want to speak intelligently to people in coverage areas I'm not extensively familiar with; would it be okay to ask for a sample of a deep dive paper to express interest in what they are doing, or does this break rules on inducement? What can I do to ensure that I'll get an email or a call when the time comes?

Luck is when preparation meets opportunity. My concern right now is just finding the opportunities since you can never do enough preparation.