There is no way to just transfer cellular service to a watch from an iPhone directly. The iPhone shares its service with the watch, but cannot simply transfer it to it.
The iPad gets messages and calls from a working iPhone. It will not get them on its own. Same thing happens with a watch.
Apple can forward the calls from an iPhone to a watch while its working, but if its not working then the calls simply won't be received.
You can set up a watch to have its own cellular service separate from that of an iPhone, through family setup, but you still need a working iPhone to set that up and it will have some limitations.
click here ➜ Set up Apple Watch for a family member - Apple Support
If you can borrow a working iPhone from someone you can use it to set up the watch. But you will need to erase the watch first.
click here ➜ Unpair and erase your Apple Watch - Apple Support
coluch5 wrote:
...but I'm looking to see how much functionality I can retain while mainly pulling the phone out of the equation.
You can, remove a personal iPhone out of the equation, but you still need one to do anything with the watch.
Like I said, you can set one up through Family Setup, but that will be limited and still need access to an iPhone (does not need to be yours) to do that, and a carrier that supports stand alone watches.
Otherwise, no, the watch is not designed to work without an iPhone.