Need Help in Networking Strategy

I am from a small non-target school and I am looking into applying to the usual (MBB and tier 2 firms)

First of all, I am very confident in my resume, experience, and interview skills because I was working on those all summer.

When it comes to networking, what I have been doing so far since mid-July is emailing school alumni and networking with them. We talk about their career, daily life, etc. And some of them, thankfully, told me to send my resume so they could refer it (Only so far: BCG, Accenture and EY, but I didn't hear anything back yet)

But at this point, at the end of the summer, I ran out of alumni to talk to because it's a very small school.

1. So what should I do next? Should I email people who work at these firms (MBB and tier 2) or is that in appropriate? Because I saw one of the most famous posts on here said "Never reach out to someone who's email is not public". Or what would be your strategy to get an interview?

2. Also how could I make my networking calls more efficient. Because out of the 25+ people I talked to, only around 8 or 9 told me to send my resume. Maybe because I don't ask them to, because I read that it's rude to do that on the first call.

The problem is that time is ticking and I know that this next month is very important and I need to get interviews :(