What you want for $2/month is unreasonable. I pay more than double for FastMail.

As the article explains, it won't even cover the base hardware costs. So you won't be "paying your part". The only reason to offer something like this is to "up-sell" to an actual properly paid plan, and since you will also lose quite a large percentage to payment processor fees, have extra support/admin overhead, deal with users who now feel entitles to "paid support", having a $1 or $2/month price point is just not worth it.

You will either need pay for it, or do it yourself on a cheap Linode VPS or Hetzner machine or whatnot.