There's no way, with the technology in orbit, that they could introduce a workable charging model. The defunct European navigation satellite venture aimed to provide a 'chargeable' service (Galileo) but it failed (unsurprisingly - how can you charge for something that's available free elsewhere? Their encryption was also cracked almost immediately meaning you could have got it for free anyway). What they could do is reintroduce selective availability (like we used to have) and perhaps have a tiered system where you pay for greater accuracy. And of course there is always the option to hit the 'war' button and turn off civilian access completely.
It remains to be seen what will be done as the current network of ageing satellites are upgraded / replaced - it wouldn't surprise me if the USAF didn't start to want financial contributions from other countries governments (and they would of course pass this on via taxes) - after all it's a global, free service which the US taxpayer is funding.
I would've thought the simplest model for charging would be to include a licence fee when buying the receiver - every new unit includes a fee to go towards the system. Keep it simple - just on new units, as a one time charge.