*The Supernatural Mercenary/Security Group
Regarding problems, it doesn't necessarily have to be wealthier folks, but if you do handle wealthy clients, you can afford to handle smaller clients pro bono or close to it. Similarly, handling a few big cases with big income frees you to work on other cases with the other player's characters the rest of the time. Remember, it isn't all about your character, and you don't only have to work on your cases.
See also 'Company Troubleshooter'
*The Dresden Technique
Nothing wrong with this. Very similar to some of the other methods.
See also Supernatural Mercenary/Security Group and Company Troubleshooter
*The Batman Technique
Why is there a problem connecting with society. Peter Parker is a photographer and student. Clark Kent is a reporter. In addition, you aren't all by yourself, you play with a group, right? Your group members are part of your 'contacts' and part of how you will get involved with things.
For contacts, you mentioned The Shadow. There was an old TV show called Stingray where the person did something similar, working for an unspecified 'favor' in the future, and he always had contacts this way as well.
*Community Figure
You can still be a community figure in a large place. Most cities are broken up into loose neighborhoods, and people tend to stand out among their smaller communities. They are people who set up youth centers, turn abandoned buildings into useful community areas, organize neighborhood watches, run soup kitchens and more. Get enough renown and people will come to you from farther away, too.
*Company Troubleshooter
Heck yeah they could do this. I would say he wouldn't work for one particular company, but would be the contact on the other end of a discreet phone call to 'clean up' a problem. Put another way, do you think that no company has ever used a hit man or similar connection to rough someone up or worse?
See Supernatural Mercenary/Security Group
Now I want to say something about this in general. Basically, many of these, except 'Community Figure', are variations on the same theme. You will get 'jobs' or leads, at least, based on contacts and the other players.
I'm going to revert back to the 80's for a minute. Most games are, I think, more like "Magnum P.I." than either "The A-Team" or "Stingray".
A-Team
"(Ten years ago / In 1972), a crack commando unit was sent to prison by a military court for a crime they didn't commit. These men promptly escaped from a maximum security stockade to the Los Angeles underground. Today, still wanted by the government, they survive as soldiers of fortune. If you have a problem, if no one else can help, and if you can find them, maybe you can hire... The A-Team."
Stingray
http://en.wikipedia.org/wiki/Stingray_(NBC_TV_series)
Single mysterious individual travels the country responding to cries for help from the few people who have learned how to reach him.
Magnum P.I.
http://en.wikipedia.org/wiki/Magnum_piA graduate of the U.S. Naval Academy, Thomas Magnum served as an officer in the navy and served several tours in Vietnam as a SEAL. He resigned his commission and lives in Hawaii, working occasionally as a P.I. Two of his buddies from Vietnam, both Marine vets, also live on the island, occasionally helping him (being suckered into helping) with his cases and occasionally vice-versa.
The point of this is that Magnum and his friends are tightly connected, have some interesting contacts (from rich authors to the island's crime network to local Naval intelligence) and have their own lives. Magnum does jobs and chills (and deals with Higgins), TC runs a tourist and travel helicopter business and Rick manages a couintry club. While Magnum is clearly the main character, though, stories come from all angles, and each of the 'party members' brings something different and interesting to the table.