That's the dream! I think it won't work at most public companies unless you end up in a department with a dead-end product whose raison d'être is to keep one or two whale customers happy.
I have a friend who does migration tools that help businesses move their data from ancient versions of software that the big players don't support any more. It's a niche, but it's a niche that banking/insurance/etc customers are willing to pay for. I've applied for jobs like this and never even made it to the screening call. When I asked how she got the job, it was through a former colleague of hers. I actually interviewed with that colleague at a different company several years prior and I heard from her that his impression of me was that I would be bored in the role. So I think it's really important to emphasize to the hiring manager that it is exactly what you are looking for, especially if you have a background in more "hip" companies.
If the "boring" companies don't call you back, my recommendation would still be to look for B2B software, or an internal/tooling-focused team where your customers are your colleagues. It has to be on a product that is already profitable (or seen internally as valuable) so that you don't get pressured into adding new features or having the whole product killed from under you. Ideally a company that is not on the IPO track. There are some maintenance roles to be found in these "hip" companies, but they're rare, and I think you have to accept that you might only be able to fly under the radar for a year or two until an ambitious executive comes along who wants to reorg the department into a boondoggle production line.
