I’m afraid using the webthings.io remote access service to access your NextCloud instance would be against the terms of service, because streaming all your files via our cloud servers (encrypted) would use a lot of resources which would impact other users of the service.
you agree not to… Use the WebThings remote access service for any use other than its intended purpose of providing secure remote access to a WebThings Gateway
However, the good news is that the software which powers the remote access service (PageKite) is open source. You can either run your own server somewhere, or use PageKite’s hosted service and choose how much to pay, from $4/month.
There are other options available too, such as ngrok.
Personally I chose an ISP who will provide me with a static IP address so I can use my own domain with port forwarding on my home router. If you have no choice but to use an ISP using carrier-grade NAT then that approach (or Dynamic DNS) is unfortunately not going to work for you so I imagine you’re going to have to use some kind of hosted service as a relay.
Whilst there’s no reason for you not to install NextCloud alongside WebThings Gateway on the same hardware, I’m afraid the webthings.io tunnelling service (which is provided free of charge) is not designed for general purpose use.