Ask HN: Scriptable iPhone Redialer Interface? (For reaching state govt.)

I'm trying to get into the hold queue for a certain state government office that is (very) badly run. Long story short, you call the number and it puts you through around ~3.5 minutes of pre-recorded nonsense only to be told "We're sorry, but we have too many calls to help you at this time. Please call back later." and then hang up on you. Not place you in a hold queue, literally hang up on you. This is not a joke, exaggeration or lie, this is quite real.

The thing is, if you get REAL lucky, you MIGHT just make it through to the hold queue after all. There's a slight variation in the way the pre-recorded message plays out in the first minute or two if you happen to make it through, but it's all based on unknowable and unpredictable call volume from potentially hundreds of thousands of other people all at the same time and the line is only open M-F 8-5.

The only way to solve a problem with this agency in my case is to reach a human being with this agency and this is the only way to do it. Problem is, it's nearly impossible to get into the hold queue. I've called them, brute-force style, over a dozen times over and over again and been hung up on after the pre-recorded crap every single time. The only way to get into the hold queue is to get lucky. Which means I need a way to automate this thing for brute force so I can finally get a human.

Anyway, I've got an iPhone 12. I'd rather not have to sit here and dial, wait, hang up, dial, wait, hang up, etc. all day long trying to brute force my way into a hold queue to get to a human being, which is unfortunately the only possible way to solve my problem with this particular state government agency.

I'm not aware of any programmable phone technology interface that I could use as a one-off to automate my iPhone's phone interface for something like this, hence why I'm asking HN. Would you folks happen to know of a tool I could use for something like this? Doesn't need to be anything super formal, certainly not looking to build a product, and it only needs to dial ONE number. It just needs to be able to listen for a pattern and hang up and repeat if it hears that exact same pattern, and if it hears a variation from that, NOT hang up. Ideally something I can script from my MacBook Pro to control my iPhone, then put the thing on speaker while I go off and do more important tasks, like clean the kitchen or something.

I'm chasing down non-technology options (state senator's office) but in the meantime, I'd like to see if there's a way I can automate brute forcing my way through their broken phone system. Anyone know of any scriptable way to do this? Thank you!