The conversation with Fronobulax is useful because it makes me analyze my motivations. What do I want, actually? And on reflection it turns out that what I want is a clear plan. Secondarily I want prompt service, but mainly I just want an understanding of when things will happen, so I can plan.
There are reasons I could attach to that, like for instance I don't want them to randomly ship it to arrive on a date when I'm out of town. And if I know roughly how long it's expected to take, then I can plan for that. But when it comes down to it, I want a plan because it makes me feel like things are under control. If I know when it's due, I know when it's late; and if I know it's late, then I can legitimately pester.
I'll draw a comparison again to bringing a car in for warranty service. No car owner would tolerate months of waiting with no particular plan or deadline for completion, and nobody would accept claims that staffing issues now require it to be done that way. People might accept reasonable delays, but not a complete lack of structure to the process; they'd accept extended deadlines, but not "someday, when we get to it." And it doesn't matter if the customer really needs the car for something or not. Customers should not need special pleadings to obtain a commitment to complete the job.
Basically I have the same sort of expectations that most of us are required to adhere to at our own work. How many of us have employers who would be fine with hearing "okay, boss, when I feel like it?" In our daily lives, we have deadlines and due dates, so it doesn't feel unreasonable to expect that generally. Not being able to get it makes me feel like Guild is not taking the job seriously, which increases my tension level about the whole thing and spurs me to call them again.
Thanks to Fronobulax for making me think this through.