Interior home renovations. More specifically, a subcontractor who specializes in demolitions.
Home renos generally have less view to the public because much of the work is happening inside. Because they're usually carried out by contractors who are paid by the job, not the hour, there's less focus on timekeeping, and it's not unusual for them not be there at any given time, or even a given day, or working late, or whatever.
If you have the place to yourself, you can go to town: you don't have to work taking down framing if you can simply pull the joints apart instead of having to use tools to pry them, so what might take someone else the whole day you might get done in a few hours. Pull whole cabinets off walls, move stuff around that might require two or three people, and do it faster than a normal human could. A job that might normally take three days, you can do in two; at least that's what you tell the contractor. In reality it might have taken you only half a day.
Just as an example of what I mean, consider taking out an interior, non-load bearing wall that, oh, let's say 12 feet long. The wall will consist of 16 studs, ceiling and floor plates. If I'm taking it down, once any drywall or whatnot is removed, I can take a Sawzall to cut each stud out top and bottom, then get a pry to take out the plates. Or I can take a wrecking tool, twist or knock each stud out, then again with the prying. Either way, probably 10-15 minutes, at best, for an individual, and then there's a load of scrap material that will take a few trips to move out of the way.
If I have super strength, I can twist out two studs at a time, one in each hand, put them down, and move on to the next two, which takes a few seconds. Ceiling and floor plates? Grip the wood and rip them out. Another few seconds. It might take me less than a minute, and then I could carry the whole lot out back to drop into a dumpster or scrap wood pile all at once. All in all, 20 or so minutes of work done in less than 5.
You do that, you become known as the person to call when they need a demolition done quickly. Because you're a subcontractor, the property owner doesn't deal with you, and you're doing a job that has to be done before all the other trades come in, so less risk of someone else being there.
ADDENDUM
It occurred to me that the problem of other people involved in the same job site finding out the secret is if the other people on the job site are already in on the secret.
All of the superheroes who don't fall into the unsponsored/independently wealthy groups are going to face similar problems, so the solution is obvious: team up. Lady Superior, with her superstrength, doesn't have to worry about the main contractor walking into the place where she's doing interior demolition because the main contractor, Jim, is far better known as the flying Skymaster. Jim also employs Alan as an electrician (Alan being the superhero Electostun), and so on. In fact, this is one of the secret benefits of joining a superhero team: they provide support and training for the whole crime-fighting thing, but also skills training and job opportunities for civilian life through the various businesses the team runs under the table.