You run a dynamic DNS script. It reaches out to the DNS server (provided by whoever registers your domain name) every five minutes and says "my IP is x.x.x.x".
The problem is that it takes a few minutes to update when it changes. That might not fit your use case.
I think they're thinking "shit I can barely survive and have two jobs and I don't want my kids to starve and I'm taking care of my elderly parents. I can't go riot or my whole family will suffer."
Your Verizon router is the farthest "outside" your network. Your firewall will be 'inside' it. When you connect them, you're connecting the router's LAN (inside) to the firewall WAN (outside).
When you don't have a lot of money, you often get hand me down clothes that don't fit. You then make do with what you have. And if a group in that situation adopts it as part of the culture, it can become cool and starts to be taken in fun directions.
Look at ripped jeans. It used to be a sign of poverty (you can't get new jeans and your parents can't fix them?), now they sell it as a feature.
That said, it's no more ridiculous than ties and buttoned collared shirts. Asphyxiation is a weird cultural fashion.
I know you're looking for self-hosted, and I hope you find it. But in case you don't, the free tier of calendly might do the job. I used to use it when I was job hunting.
You run a dynamic DNS script. It reaches out to the DNS server (provided by whoever registers your domain name) every five minutes and says "my IP is x.x.x.x".
The problem is that it takes a few minutes to update when it changes. That might not fit your use case.