Just a little idea that I think fits thematically, would be for there to be a few different favours you could 'ask' for when using PFs besides removing all Jail time. Of course you can only choose one per Favour.

A desirable choice would be the ability to reveal the cash-in-hand and Battle Stats of a player, maybe with a 100% chance to reveal one random Stat, 70% chance to reveal two random Stats, 40% for three, 20% for all four or something like that. Maybe a possibility to reveal their Dog Stats might be useful in some way? 

Another use could of course be to make yourself unable (or much less likely)  to have your Stats revealed for, say, 48 hours, or long enough to be useful, but short enough that they would keep getting used up by active players who want to stay covert to stop the market getting filled up with them.

It could also make a nice divide between players who like to grind the Standard Jobs specifically to earn Personal Favours, and those who prefer grinding Robbery Jobs, so that neither market becomes too saturated but both are worthwhile enough to grind.

Maybe there are some other uses they could provide that I'm missing.

I really quite like this idea. Perhaps rename the current PFs to something else, for example, Get Out Of Jail Free Cards (or whatever)

And then use your idea for the PFs as a seperate thing would be kinda cool.

I also think this is interesting, you have my thunbs up!