3. the From: address is the owner/mod, not the group addressI think this is a bad idea (unless you mean the group's +owner address).
The problem is that the receiving service will look at who delivered the message (Groups.io) and who is named in the From (somemod @ example.com) and treat the message as having been "spoofed". This will probably make the message more likely to be delivered to the spam folder, the opposite of your intent.
A message that is honestly from Groups.io, or better still a message direct from the mod/owner's email service, are almost always more likely to be delivered to a person's Inbox than a spoofed message.
Suggestion 2 does not require the member to go to any web page, theyI like this idea. Along with your later suggestion that 1 & 2 could be combined: a single message that lets the (former) member choose whether to reply by email or click the link.
I would suggest that the resubscribe command email does not generateThis is already true of the notice containing the resume link. So that should be easy.
This would require groups.io to retain knowledge that the member wasThis also must already be true for the resume link to work.