There's a reason your music industry friends aren't exactly falling over themselves to introduce you to label people. It's not because they hate your or because they think your band is bad. In fact they probably like you a lot and think your band is excellent. What I'm going to delve into here has some harsh truths, but moreover asks you to look at things from someone elses perspective and once you do that a lot of this is going to make more sense and pay off for you in the long run. Don't take any of this personally but rather use it as a way to better think about the music world so that you can make the moves you need in order to succeed and achieve bold new levels of success out there rather than muddling along with everyone else who moved to Brooklyn or LA or Austin or wherever to 'make connections' and ends up never getting signed to a label of any merit. You might need to change your perspective, but that's part of the fun.
Now I want to be clear, if your music and branding is good enough it doesn't matter who you know, people will come and talk to you about a deal. Simultaneously if your music and branding is terrible and no one thinks what you are doing can be sold then no matter how many label people you know or talk too you won't go anywhere. That's because people know what sucks, it's built into anyone who is trying to be successful at artist development. Music is what we're selling after all. You have to remember though that the people who work at labels etc are generally speaking, music nerds and the kind of people who will always push to create bigger and bolder futures for themselves and their organizations. This means they are looking for music. So like I said - if you're good enough you're going to get discovered if you get seen. That's what you can't count on though - getting seen and then heard.
So if you want to get seen and heard by industry people, the best way to do it is not ask your one vaguely connected friend a million times to introduce you to labels. That's just a way to piss off that friend and get yourself made into a laughing stock. If they think you are good enough they will do it without you asking. Tied into this - realize that the reason they are hesitant about pitching you to labels is because they are dealing with a relationship. They don't want to be the person who is out there constantly trying to get the dude at Sub Pop to sign their friends bands. That's not how it works. If they kept doing that the dude from Sub Pop would just think they were a pretender and trying to take advantage of them and would stop wanting to hang out. Odds are your friend with connections likes having friends, so if they are smart they are going to be extremely recalcitrant to connect you to people until it's clear that everyone benefits.
If you have a friend who has industry friends and hangs out with those people a lot, maybe just hang out with that friend more. They will introduce you to their industry friends just as another musician, and then you can stat to cultivate a relationship. You will become one of their friends and someone who is tied into their whole brand. This is really important if you are trying to connect with people and level up where your band is at. If you don't live somewhere where the music industry people are that doesn't mean that you can't find other effective ways to be. For example, if you go to festivals, even as a fan the odds are that you will be able to befriend some industry types or at least people somewhat connected. Again don't go around expecting people to immediately hand you a record deal, but please do talk to these people. They are passionate about music and like connecting with artists, they work in music for a reason.
In the music industry we are dealing with a very finite amount of resources and everything being based around relationships. If you're not 100% confident in a relationship then don't ask for anything. If you're not 100% certain that your music is exactly where it needs to be and it sounds polished and good to go then you are going to get ignored. I get countless great bands sent to the Prophecy and Ripple emails every day. If things aren't all lined up though I'm not going to dig in. If they have already built a relationship with me built on, not being a sycophant, but instead mutual respect then you start to see where you will get a chance to grow. There are a lot of people out there who think being a sycophant adds to your relationships, it doesn't. Instead just be a person and realize that maybe people don't hate you or think you are terrible, you just don't fit for them or their connections right now and that's totally okay.
Don't go out constantly expecting hands outs. People who are regularly coming to me begging for me to do something for them beyond giving advice are going to piss me off and they are going to piss off other people who are connected. Not only that but they aren't building the relationship. People who build the relationship just by wanting to talk and being cool people are going to get a lot further. Relationships can be viewed as transactions and if you are only asking for things and not contributing anything then why should the other person be expected to contribute? If you DO bring value though then people will grow with you. It's a rule as old as time. Build relationships and make friends. It's great.