Fix it yourself.
All kidding aside, what is stopping you from doing just that? If you are capable of doing so and were to try to fix it yourself, how much time would you spend troubleshooting, tracking down parts, etc? As the owner of a service company, it's incredibly infuriating and demoralizing when we hear a customer "I could have done it myself in half as long as it took your guy to do it!" while ignoring the time spent troubleshooting, tracking down parts, checking for safety / functionality and cleaning. Did you approve or sign their hourly rate sheet on the front end before the work began?
Now, to play the other side of the coin, it does not sound like this service company has been transparent with you, and many companies put people out there who aren't the best and either screw things up or basically get paid to learn on the job. Or, they have shitty processes that rack up hours without any work getting accomplished. I'm guessing your experience is rooted in one of these. We constantly ask our employees to present "clearly communicated realistic expectations". Sounds like they failed here. If they knew it may have taken three trips, they should have communicated that up front as a possibility. And, if they're learning on the fly, they should be transparent and receptive to billing at a lesser rate. My guess is this is a larger company with an absentee ownership group who's simply trying to hit a metric for hours billed with no common sense oversight on individual transactions and a lack of empowerment for that tech to make those types of decisions around discounts, etc. We see that a lot when service companies are big and fragmented.
So, where do you go from here? Are there other service companies you can try? Or, are you essentially starting over if you bring someone else in at this point in the game? I'm dealing with that exact scenario with my AV guys. They were awesome when they did the install four years ago when we built our house. Now, their service absolutely sucks. I've been waiting two months for them to replace something that is sitting in their warehouse. They send over new people every time I schedule service and they're basically charging me to re-learn my system. It sucks, but I'm between a rock and a hard place because I don't want to pay a different company who won't cover the existing warranties and would really need to re-learn everything.
That being said, I'd reach out to your service company and try to be nice at first. Explain to them the situation and see how they react. If that doesn't work, then escalate. But, you have to ask if that extra time and energy solves anything and ultimately costs you more in the long run.