You eliminate the rural area with 5 minute drives between homes. Japan has a much higher population density more generally, granted, and they do occasionally get older, offset, single homes that are miles from anything else. But they also have extremely rural villages with maybe 2000 people that are still about as rural as you can get and still go in for farming. Many other places (I would say, basically all of them?) do this as well, and not all of them have high population density. I think, almost definitionally, the land use I'm proposing has a higher pop density, but the style of development generally, you'd be hard pressed not to classify it as rural.

The solution here is to orient the land use radially. Also probably to use less land generally, but that's a separate issue. Most land use in america looks like having 20 different farms, that are each like 3 or 4 miles across, sometimes with multiple plots, with each house being positioned as far away from the other houses as possible, usually somewhere along the edge of a plot, and then running roads out to each of them, sometimes dirt roads, sometimes paved, usually some combination of the two for higher use vs lower use vs private.

Instead of that, you do what people have been doing for centuries. You clump the 20 different houses together in one contiguous strip that's placed along some sort of rail line or higher traffic road, and then you disconnect all the plots of land from the particular houses. Ownership doesn't necessarily have to correlate with one plot of land vs another. Then you gain all of the benefits that entails, and if everything is laid out sensibly, then you're only about 3 miles from your specific plot. Utilities become cheaper to maintain, emergencies like fires, medical problems, natural disasters, become much easier to deal with, you can start building some actual infrastructure, like, say, a rail line.

That becomes much easier to justify if you only gotta send that shit to like one concentration of 20 or 30 or houses instead of sending it to those 20 or 30 houses individually, most especially if that line is just passing through before heading somewhere else, which should generally be the case. Maintenance of that rail line also becomes less problematic compared to that of a road if we're considering that this rural area is probably mostly going to be farmland that demands larger industrial equipment shipments, and is going to be shipping back and forth things like grain, bulk goods which would do much better to be shipped by train compared to most other forms of transit. Slap that together with a multi-daily passenger rail line that passes through it as a stop and you're pretty much set.