How do I change my profession? I picked tough but that one is far too low to do me any good.

Is there an option to write a letter in your Lodgings? If so, you can quit your current profession there. After that you can either pick up another training profession if another stat could benefit from it, or you can wait until you draw a connection card to pick a more advanced one. Read through this thread if you wish to learn more.

You go to your Lodgings and select the “Write Letters” storylet. That will let you end your current Profession. Then you should keep an eye out for one of the Opportunity cards that lets you pick a different one.

I would have liked to pick Enforcer as my profession (seems to best fit my character), but it seems that this requires either “Plotting against the Masters” (via the revolutionaries) or “Favoring the Cheery Man” (via the criminals). Unfortunately, I don’t have these particular qualities since they were determined by choices made a long long time ago when my character was very new to Fallen London and not all consequences were understood.

Does anyone know a way to regain one or both of these qualities?

I’m afraid you are out of luck there if you can’t get your Shadowy down low enough to draw the ‘commission from anarchists’ card. It has a cap, though I’m unsure of where this cap lies.

That’s a shame.
Choosing a profession is an interesting new mechanic, and it’s really unfortunate that some of them are locked out just because of arbitrary options chosen a long time ago which are now irreversible.

D’you know, I’d be inclined to report this one, just in case the inaccessibility is an oversight. After all, while Cheery Man/Last Constable is a deliberate story choice, there’s no reason one couldn’t start Plotting Against The Masters just because one has become sneakier.

Come to think of it, Enforcer seems to be the only one that is affected by this. All the others have alternate paths that you can take, with the possible exception of Journalist if ‘Raking the Muck of the Neath’ has an upper Shadowy cap. Perhaps the commission from anarchists can have its cap removed?

Edit: Yes, reporting this matter would be a good idea.
edited by Sara Hysaro on 2/20/2013

Alexis has said that there are changes coming from the new broad challenge model that include allowing higher stat characters access to lower level content again since it will no longer be trivial. This may solve itself eventually.

Also, there are more professions coming (another one of the things on the to-do as follow-up to the latest vision Alexis laid out).