I've been tossing around the idea of starting a group of people who are committed to buying Bitcoin every month. Can be a small portion, like 5$, or however much people can afford (I suppose it would make sense to use higher amounts for fee reasons, though). I myself have set up a monthly wire transfer from my bank account to Coinbase and a recurring purchase of Bitcoin every 1st day of the month. This is really simple, and you keep investing and $-cost-averaging your BTC purchases.
Who's in?
I created a Google Form where anyone who wants to "join" can do so: https://forms.gle/rjD81677yipAVhtaAThis is too risky and not sure if this will work out in this volatile environment as what you are planning involves money from a group of people and you will be held responsible if things don't go well because most of them might not invest small amount due to the transaction fee as you have already mentioned and there are some people who might be concerned about their anonymity as well. Anyways all the best with your project but please do give it a second though to eliminate the risks and start with a small group of users like your friends and then grow the group gradually if it works.