Hello Star Tech,
The variety of equipment has become so vast that I stock very few parts on hand. The old days of common stock parts have passed. I get what I can local, but a majority of my parts are ordered online these days. Even the dealers have reduced their parts stock tremendously. In your case it would have been easier to get a complete (expensive carburetor) then a simple mixture screw.
If a customer expects same day for any in depth repairs, it's just not going to happen. I explain the situation up front and if they are in a rush, maybe they will have better luck somewhere else, but that is seldom that works out for them.
As a good automotive mechanic friend of mine says quite often: "I did not buy it, build it or break it, all I can do is fix the machine if allowed the proper time needed".
A self-entitled customer throwing a tantrum or tapping their foot impatiently while surfing their phone does not phase me these days. If they get belligerent, that ends all conversation immediately. I do not suffer fools well.
Dealers this time of year are swamped to a point where they often turn customers away unless the machine was purchased from them. Even then it may be a 2-3 week wait (or longer) before it is even brought in for evaluation.
Most independents in my area have folded because it has become so hectic and they are just fed up. Poor quality parts from the aftermarket and even the dealers have become a huge problem post COVID era. When it takes a couple of times to finally get a good part, all profit is lost.
Years ago, when I was a service manager at a JD dealer, I would cringe every time a (fun) 3rd party extended warranty job would come in because the warranty company wanted to dictate the repair terms and cut corners.
I hated to do it, but those kinds of jobs typically got moved to the back of the line because they took so long to negotiate terms and get approvals for repairs. It really hit the fan when the customer expected repairs to be fully covered... Often time the customer had to pay a deductible or the difference in cost of the repairs. Of course, they never read the contract.