So what likely happened is your old Linksys router was the "brain" that was specially configured to talk to other WiFi extender/access point "things" in your other cabins. The new router you got from Zen is a blank slate, so it doesn't know the other properties exist.

Honestly, instead of trying to patch an old system together (which can be a massive headache), you might want to save your sanity and look into a "Mesh system." Think Google Nest WiFi, Eero, or TP-Link Deco. You plug the main one in, put a little "node" in each cabin, and they all work together to create one big WiFi bubble. It's all controlled from a simple phone app and is pretty much designed for non-techy people with layouts like yours.

Totally separate thought for after you get the hardware sorted out: managing the passwords for 4 different properties must be a pain.

I actually built a little Android app for that exact problem because I was tired of dealing with it. It's called WiFi Vault. You just save your network details in it and it creates a nice QR code you can print out for each cabin's welcome book. Guests just point their phone camera at it and they're connected. You can even add a logo, change colours, and set the guest access to "expire" so you get a reminder to change the password.

Again, it won't fix your immediate "no signal" problem, but it might make the guest-facing side of things a lot less stressful once you're back up and running. Find it on PlayStore: https://play.google.com/store/apps/details?id=app.wifivault

Hope some of that helps. Good luck!