Hostinger is the closest I can think of. They do have limits but they are very high for the price (which is actually true of dreamhost too, they just aren’t honest with you until you hit them).

Just use a free mailjet plan

Here’s a decent list on awesome-self-hosted

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mesh networking like zerotier or tailscale is usually a better option for homelab scenarios. Maybe that will be helpful.

check out vouch proxy.

This is the right answer.

The only other solution I can think of would be to put a device in the middle (such as this router).

Maybe caprover gets you close to this?