My experience . . . best to have a date as early in the day as your processor will take them.
Withholding feed, in my book anyway, is a practical matter of having the crop and a lot of the gut empty. Honestly, though, food in the tract presents more of a challenge to me, the amateur butcher, than to the folks who process my large batches. Doesn't slow them down a bit and I've never seen them cut into a crop or intestine.
Still on the practical side, withdrawing the food and processing early in the next day can go hand-in-hand. If you factor stress on the birds into it . . . if you withdraw their food the evening before as they go to roost, they wouldn't be bothering it overnight anyway, and they'd have the night shift on their roosts to eliminate a lot of it, which would address the matter of emptying the crop and a good bit of the gut. Yours are not (as you've said) meat birds, but the disruption would be even less to any CornishXs who are accustomed to a 12-on/12-off feeding schedule.Though it's not a concern to me, that would also address the issue of the economics one of us brought up, about the cost of feed that will never be productive.
Then, if you get up early to take them to the processor, you've minimized their stress at not finding any feed around when they hop down in the morning. The trip will be stress enough. Birds can be conditioned to a lot of things, but I don't think that motorized rides are a regular event in many of their lives.
I'd recommend withholding feed overnight before their trip to freezer camp. As I hope I've described, an overnight, something like a 12-hour, withdrawal should minimize the stress on them, with the added benefit of making them easier to handle than if you withheld for a whole 24 hours. I don't know how yours behave, but if mine hadn't had feed in 24 hours and I opened the door to the yard or the coop, I'd have one heckuva challenge keeping them contained as I rounded them up. Especially with all of the opening and closing of the door or gate as rund them up. If you get to them as they're just waking up, they'll be a lot easier to handle and crate up for the trip.
My two cents.