In thinking about it, I suppose one way I could do it would be to delete my eero network, switch out which of my nodes is to be the gateway, and set it back up again.  That way another MAC address would be coming through in the public DHCP IP request and I'd (in theory) get assigned a different public IP address.  So it would seem that there's a manual workaround that would require me to nuke my eero config each time this is required.

Thanks, cMoo92.  Good to know. I didn't know I could just juggle the eero units around and they'd figure themselves out.  Might have to try that the next time I get assigned a bum IP address!

Matt Not in the way that I think I expected based on what was said above.  What I had hoped would happen is that if I unplugged the gateway from the modem and plugged in one of the other two non-gateway units to be a new gateway, and just connect the old gateway to power only, one would automagically understand "Oh, now I'm the gateway!" and config itself as such, and similarly the former-gateway that is now not connected to the modem would say "Oh, now I'm no longer the gateway!" and configure itself as such; basically the whole system would dynamically configure itself accordingly.  That is not what happened when I tried it...  

What did work with less hassle that completely deleting and recreating the entire eero network was that I moved the ethernet cable that connected the gateway unit to the cable modem from one of the gateway's ports to the other (then power-cycled everything including the modem).  That caused a new external IP address to be assigned, when doing this without switching ethernet ports would not have.  So that was what I needed.  Switching ethernet ports on the eero gateway apparently changed the MAC address involved in the dynamic IP address assignment process so my ISP saw it as a new client and issued a new IP (reserving the bad IP address for the previous MAC address for some period of time until that old reservation expired).

There are two different DHCP's at work -- one from the perspective of your ISP, giving your router a dynamic IP address on the WAN, and that's completely separate from what goes on inside of your network -- where your router gives out dynamic IP addresses to the devices INSIDE your own network on your LAN -- again, thanks to DHCP.  One doesn't impact the other, except for when your router gets a new IP via DHCP from the ISP, it might need to synch up your LAN devices network details with any new WAN details (DNS servers? not sure).  Really, most of your LAN clients typically use your router as the gateway and as the DNS server, so probably not much if anything really makes a WAN IP address change impactful on your LAN devices, the router does all of the. middle-man stuff there.

I get what you mean by "sticky IP" but that's only because of your ISP's DHCP lease time, which makes and hold reservations by MAC address.  Once your MAC address doesn't show up for more than the lease time, the lease expires, and it will release the IP it's reserved for you on that MAC address back into the assignable pool.  Releasing it doesn't mean that you won't get it back -- it means it's available for ANYONE to get the next time someone unknown makes a DHCP request and it's selected as the one to be given out.  It could be to you, it could be to someone else.

I'd recommend reading up on DHCP, it's pretty interesting stuff and you've clearly got more questions than I would have time to type out answers to...  Or ask these on a relevant reddit thread since they're not eero specific? 

(It's not that common for someone to need to change their public IP address very often, usually that's because of downloading or hosting torrents or other (ahem) activities.  Just get a VPN...)

Good luck!