How long does it take to push a 368 form to be released from the SC National Guard to Active Duty?

There is no set in stone length of time. The timeline for the process varies from command to command. Ive seen it take as little as two months and as long as eight. It will have to go up through each layer of your Chain of Command and then back down.

It takes as long as it takes for the authority to sign it. Just like an award, it only takes minutes, but it can take months. That's an SCNG internal question that no one here can answer for you.

It takes as long as it takes. When dealing with the National Guard things can take along time, because it is a part time activity.

Have you thought about "walking it through?"

You may or may not be able to do this; but i do remember having a soldier once do this in my unit, it was easier for him because we had so many active duty people (as an enhanced unit), he went to his readiness NCO, who signed off on it, then to the BN XO who was full time guard for the unit, and then he "walked it" to personnel. Once it got to state it took less than 30 days to turn around. He was gone the next drill.