Its possible that Charlie had some other gimmick in mind like bringing in captured archons via Haggar. (assuming that being captured allows you to now move on their turn even though yours is over or hasn't started yet)
Or Charlie thinks he can wait till beginning of next day, when he has a turn before Parson.
Well yes, BUT, the point of getting Faux Slately to the throne was to turn off the portal BEFORE GK has control of the garrison. Once GK has control of the garrison, the portal would close anyway. Ergo, part of the plan is to cut Parson off without a retreat before he can take the city. RIght now the inferno is enough of a reason to do that but that wasn't part of Charlie's original plan (barring Predictamancy).
Actually, I think you've put your finger on it. That was exactly the nature of the trap, and Predictamancy is the key. Using Predictamancy, Charlie would be able to know for certain that Sylvia the city was going to burn to the ground, just not how or why. Logically, Parson wouldn't hang around to be incinerated while the portal was open, and once the the city was captured and the portal closed naturally, he might be able to put it out, if he had a Dirtomancer on hand. Therefore, let him come through on his own, and then have Slately switch capitals to close the portal. Case closed.
Sounds like a quick and dirty fix to me, and it certainly caught JoJo on the hop.
It seems to have worked too. I don't have a clue how Parson is going to get out of this but I Predict it's going to be a doozy.
.. one solution would be to capture Jetstone and have Stanley switch GK capital site there, opening the portal again, so that Parson and Jack could escape, or maybe Sizemore could get in and put the fire out. It would be a hard sell though. A variation on that would be to switch the the capital site after the city had burnt down and croaked or dusted everyone inside. Then Wanda could come through and decrypt Parson, Jack and the whatever remained of the Jetstone troops. (including the Dollamancer) That would be really nasty though.
Or maybe the New Side option works.