Seems like you have thought it through pretty well. Not being there to observe is kind of a handicap for giving advice.
Just throwing some stuff out there. I've actually had better luck pass shooting than trying to shoot a flock. The flock scatters every time you shoot and it can take a while for other Doves to come in or the spooked ones to return.
I'm thinking there may be more birds there than you realize. They just come through in dribs and drabs.
What about setting up a blind between where they roost and food or water? Try to spot the flyways and set up our blind there.
I had a really good spot between two low hills, the Doves would come through in singles and pairs over a saddle between the two hills. They were on me before they could react. Two to three hours in the morning and I'd have my limit. I've had up to six hunters in that spot and everybody got there limit or nearly. It really didn't seem there were that many birds there, as you wouldn't see them in flocks at the food, which was over the hill.
They tend to make a Bee line to food, water and to roost. And generally fly low, especially after they have eaten in the early evening.
The least productive hunts I've had is trying to get close enough to shoot at a feeding flock. I may get a few birds, but not nearly as many as hunting a flyway. Just a guess, I'm not a Dove, but birds often feed in a flock because the more eyes the better the chance to spot a predator. Once they scatter it can take quit awhile for them to re-gather. I have had reasonable luck setting up near a roosting site in the late afternoon and early evening.
What is the soil where you are at? Red clay? Maybe fifty pounds of mortar (washed) sand spread out someplace between the food and the roost will channel them to a specific spot? And maybe a few decoys on the sand?
Who is to say whether you are mulching or knocking down the grain? I guess a really anal Warden might say something, most just want to check your license, if you have shot too many birds or to check what ammo you are using.