This could work, this is an actual decent plan, except those farms are going to be the first thing they go for. That's why I was talking about the Special Forces, they are experienced in this exact field. They specifically, during the Troubles, killed off farmers who were friendly to the IRA and buried them in their own fields, or harassed them into selling up and giving their shit over to state-friendly owners. As far as I know, the USA doesn't have a specific military group who engage in outright illegal activities against their own civilians, whereas the UK does. On-the-ground espionage against their own citizens to arrest or kill potential rebels.

"Hey Steve, you know how the Anderson Dairy farms been run by the Andersons since the town was incorporated?"

"Yeah, what about it, Bill?"

"They didn't come by church, and Chuck ain't seen them at the feed store all week. Do you think it has anything to do with the strangers with funny accents that we, as small town folk, immediately pegged as interlopers?"

"The ones that showed up after the civil war went hot?"

"Yeah, thos 'uns. You don't reckon they did something unseemly, did you?"
-A Short Time Later-

"You strangers need some more coffee?"

"Yes, we're thirsty from uh, managing the old Anderson place, which we bought without anyone knowing about it!"

"Oh, darlin', looks like you boys are just exhausted to boot, passing out right in the diner."

"Must be all the poison I put in your coffee!"
I'm just kidding, I'm sure that the Coastal governments will be able to control the 900+ million acres of farmland in the US and turn every last inch of it into an impregnable fortress with zero problem whatsoever.
You are 100% correct, the USA needs these rural areas entirely, that's why they will do everything they can to make sure those farms are protected and nobody can interfere with their power structure. They will set up checkpoints near to the dairy farms, and at best you could snipe some cows from a distance.
Yes, I'm sure that they will also be able to protect the literally thousands of miles between the productive farms in the middle of the heartland and the major coastal cities. There won't be a single opportunity to disrupt the flow of milk and corn from the massive fortresses of Wisconsin to New York or LA. There aren't any infrastructure bottlenecks like bridges or mountain passes, or long lonely stretches of highway that pass through rough, difficult to patrol terrain. If there are any, they will be patrolled day and night by the millions upon millions of soldiers that will just....be there magically because in this special civil war the rural people must lose, facts be damned.