Back in the day, I did a lot of MUSH/MUD roleplay (shoutout to AmberMUSH) and a fair bit of RP in World of Warcraft. As such, I've been thinking about how DramaSystem could be adapted to the needs of more freeform online role-play. I'm mostly coming from the chat system point of view, but I suspect you could make this work for freeform forum roleplay as well.
First off, the big things that must be changed!
1. No GM. This is usually an assumption of the form, and it's important because it removes the dependence on any single person. If you require a GM for any scene, you're losing the ability to find play more or less whenever you like. Even in freeforms where there's a GM, they play a role for big climatic scenes and aren't required for the interpersonal stuff.
2. No fixed scene flow. This is for the same reasons; in a freeform, you get as much roleplay as you can be around for, but you can set your own pace. I think this is the trickier problem, since you don't want to let players purposefully or accidentally generate drama tokens at a rate completely out of synch with other players.
I think the lack of GM is easy to handle. Freeform RPGs already function perfectly well under these limitations. DramaSystem lends itself pretty well to the idea of "prop coordinators" -- you can let players take ownership of an NPC or an institution and control it without any fuss. Possibly it should cost a drama token to take ownership. I think I'd also require prop coordinators to participate in the token economy for their prop; i.e., if your prop says no to someone's request, it costs you a token, just as if it were your PC.
The pacing problem is more difficult. You don't want to limit the number of scenes someone can call; again, that's an artificial choke on enjoyment, which is no good.
But I think you could place a limit on the token economy. To wit: any given pair of PCs can only engage in one exchange of tokens per week.
So let's say I like roleplaying with Rob a lot. I call a scene with him, since he's around to play with, and I frame it and in the end his PC gives my PC the leadership of the next planetary away team, against his better judgement. Awesome! I hand him a drama token. The next day we're both around again, so we do another scene in which his PC talks my PC into accepting the cynical science officer as my second in command, even though I hate that cold-blooded jerk. I do not hand him a drama token, because we've already done an exchange.
We can get all the roleplay fun we want, but we can't extend our participation in the currency system indefinitely. This prevents the fairly likely scenario where person A roleplays with person B every single day, and person A usually gives, and person B winds up with a million tokens.
Some smaller issues:
You need a place to capture results; this is a bit of formal bookkeeping but my instincts say it's important to the community. In some games it might be appropriate to require all logs/forum posts to be archived; in some games, you could just capture those that result in currency exchanges; in some, you might trust participants. Depends entirely on privacy expectations and so on, and different groups will have different norms.
This model doesn't have the same natural reset point that you get in a face to face game, so there's no accumulation of bennies and there's no token reset. I'm not sure this matters -- does the token accumulation make up for the lack of bennies? I'd be interested in opinions here, in particular.