I don't think there's an easy answer.
I ended up in the ER this summer due to vertigo. I called my GP a few times, left message, never heard back. I tried to treat myself with a home traction kit that made the symptoms multiple times worse.
When I finally got in touch two days later, I found out that the office had to shut down because their A/C broke.
Maybe something has happened at your GP's office. But you could try again Monday morning, adding how many times you've tried, that you need the script issue resolved, and ask as well to be fit in for an appointment that day if you can't talk to the doctor over the phone.
You might also want to reintroduce the idea of a time-release. There is none for hydrocodone, but you might want to look into Tramadol ER. It costs about $200 for 30 days.
Let me also suggest that instead of more pain meds, maybe ask for something to help you sleep. Ambien CR is a good place to start. If that doesn't work, then maybe a benzodiazepine. Although Xanax isn't typically prescribed for sleep, that's what I use because it has a relatively short half-life and so I'll not be as groggy in the morning.
Hope you get these issues resolved. I understand the difficulty trying to keep pace with intellectually demanding work while in pain.
C4-T4 Scoliosis (disk degeneration, stenosis, narrowed neuroforamen, bone spurs), RT hip and SI joint damage from car accident. Also, pectus excavatum, supraventricular tacycardia and mitral valve prolapse syndrome.
Current meds: Ultram ER 300mg & 2-3x 10mg Hydrocodone daily. Oxycodone 10mg for BT. .25-.5mg xanax as needed for sleep, Verapamil 240mg SR (for tachycardia). [/gray