Alright I’ve had a go and learnt a ton 
I set up all of the time codes in Data Jar, then had that drive menus in Shortcuts for Client and Project in Timery.
This runs as an initial timer starter for the day (called “Clock in”. If the time code doesn’t exist, Timery will create it.
Then, every half hour between 7am and 7pm, a time of day automation runs that runs this shortcut, with a couple of rules so it doesn’t ask me when I’m not working (is a timer currently running?).
If a timer is running, it vibrates my device and runs the “Clock in” shortcut, which if I select the menus on, will stop the current timer and start a new timer as per the menu selections. If no timer is running, it does nothing.
Seems to work well. I’m disappointed that Personal Automation can’t run without notifying you, as it means I’ll get a silent notification every half hour which is a bit janky, but hopefully won’t be too annoying.