I'll answer my own question here. In order to get this to work I had to do some reading up on REST data sources. I also watched this video:
Using REST Services in InfoPath, Part 2: ODATA In Depth by James Rishe (Qdabra no less)
https://youtu.be/ncN7Qr65kjI
I also had to read up on data connection files, since my form is web-based and you have to do a bit of faffing about to get REST to work in this scenario. I used this TechNet article:
https://technet.microsoft.com/en-us/library/ff621104(v=office.14).aspx
I also had to remind myself how the Secure Store works and used this article:
https://www.c-sharpcorner.com/UploadFile/Roji.Joy/how-to-enable-sso-for-web-services-used-in-infopath-form-in/
Hope this is useful to someone. InfoPath is definitely not dead to me. It's actually a great tool (but poorly documented by Microsoft). I don't think PowerApps can match it at the moment and if your SharePoint is on-prem, I definitely think InfoPath is still king. :-)