If I understand your problem correctly, you mean that ever since you started practicing for the Clones challenge and turned story progression off (for the 1st time ever), you think that SP doesn't work anymore (or not completely) when you turn the option back on? Just as if the toggle on/off button in the options panel is broken? This was a bug at the release of the game but one that has been fixed for long.
Does this happen in all your saves? If you have several Sims 3 user folders, does it happen in all of them (that could mean a "broken" options.ini file)? Does it happen only in existing saves or in fresh new one too? Does it happen in folders where you have no additional content installed? (there are "premium" items in store worlds, maybe they conflict with each other?)
For the coworkers in RH, have several Sims take jobs in different RH and use the Meet coworkers tone (to force the game to assign them) until you get the pop up that your Sims has met all his coworkers. Then switch to another RH and repeat. Yet, I think that the job/coworkers engine is not part of the Story Progression per se.
You can also try to plop lots with objects that require (resident) Sims:
Registers (Consignment shop, pet shop, WA shops)
Stylist from the Salon lot.
I think that mixologists, bouncers and tatoo artists are always homeless, so it wouldn't help here.
Another idea: delete all the living families and do the same again (coworkers, registers, stylists). With no living souls lefts in your town, the game is forced to spawn new ones. If nothing happens, you'll now for sure that your story progression is broken. If this happens in all your saves and Sims 3 folders, with or without store content, then the only thing left is to reinstall the game.
Good luck with your troubleshooting!