Be aware of any time limit on possible WC claim, just in case you do need to go that route.
But private Ins will get you faster treatment & better care, wc is full of delay & denials..and they will try to blame most injuries on past activities..so it is a battle..more so if you had high income..
WC would have to approve all tests, meds, PT etc...

I hope you can avoid that stress and get good care & resolve most of your issues..it often takes time to see improvements. And may be a lifelong awareness thing..
Sounds like you have a good plan ..