Examine the assumption that a remote access VPN is required. It might be if the IP side of this gateway does not run secure protocols. Or it might be fine over the internet, but you're having problems routing the applications.
That gateway advertises "WAN Failover" as a feature. You tried to make this into a out of band access thing, so the management interface over cell data and everything else over presumably internet. Possible they didn't test it to do this, and failover moves all features over to a different WAN link. Explore the possibilities with the vendor. Maybe in the short term you can tolerate workarounds like replacing the internet access with another device, a proper dual WAN router. Or having on site hands manually switch the WAN over if necessary.
Should this gateway's management functions not be sufficient, consider adding a remote management and monitoring service. Some of these are managed services, and would be phoning home status over the internet. Although these likely require a general purpose computer to run an agent on. If the only customer equipment is this gateway and some simple devices, that might be tricky to get on site.
Server Fault does not make product recommendations. Note that some organizations will pay a decent amount to make the VPN or RMM platform someone else's problem. Your correctly noted that self hosting is an option, but would be a thing to maintain and provide infrastructure for.