My minimum charge is $75 for the 1st half hour, but that is local, a little more if there is some travel involved. Then $75 per hour. It sounds like the question of who should pay is not an issue. The GC will pass it along to the HO and explain why it is their liability and not the GC or EC.
It sounds like the issue is the GC wants to give you "advise" on how you should run your business and what your marketing stragety should be. A six year old can see through this. It's manipulation. A per opening price at the start is entirely different from at any other point in the job. Momentum is the key ingredent that can't be quantified. It's like loading up a moving van. If you load the truck at one location, get on the highway, drive 55 to your destination and empty, you expect the task to take a certain amount of time and even estimate what's involved. But what if you were asked to load half the truck, and then pick up the rest of the stuff on your way. It's scattered along the highway. "Since you'll be driving that route anyway." Start stop start stop. Plus what if you then have to start rearranging stuff that's already packed just to make this fit. From an outsider's view, yes it is probably easier for you than anyone else to stop & pick this stuff up along the way. You have the room in the truck, you are driving the route anyway, and the stuff all belongs at your destination, but in reality the two tasks are obviously very different.
Can he hire someone else to come in and do this change? If not than I guess he is stuck with whatever your policy is. It would probably do you both some good in the future to make sure this is understood at the begining. Get your minimums spelled out in the contract.