This sounds like a carrier issue IMO. If I understand this right from Verizon when I had a issue of text messages not coming thru the watch when remotely away but calls did. They said the calls went thru because the carrier actually are the ones that forward the calls to your phone and watch, text messages and emails get sent via data from your phone, which is why your phone has to be on and connected to data for text and emails to go thru, but your phone can be off and calls will go thru to the watch.
In my case what caused the text message not to work was the setting in advanced features, remote connection was turned off somehow after a update. Took 3 plus hours on with tech to figure this out after several resets.
I'm sure you've been on with your carrier, but I would be asking about the forward feature of the calls that go thru the carrier for watches, it's a battle as most won't know what your talking about. I'm late to this party, maybe and hopefully you got this fixed. If so, let us know what it was for future issues that others could have. Everything we know about helps each other fix issues if we get, as we can't always rely on the carrier to know how to fix issues, specially on watch support.
Remember the carriers call the LTE watch plan a share line plan, so all they are doing is forwarding calls to the watch. Your watch does have a behind the scenes number which is where your carrier forwards the phone calls to your watch. They basically send calls to your phone while at the same time forwarding the call to the watch number when the watch is remote connected.
I'm assuming you don't have a stand alone plan on the watch, if you do that's your problem as you would have a dedicated line for the watch and it has its own number not shared.