Dwarven job logic is odd. I wouldn't be surprised if the stockpile targeted for plant delivery after harvest was selected at the time the harvest job was picked up. If that is the case, the dorf would probably have selected the stockpile closest (as the dwarf digs) to the dwarf's position at the job pickup time, not the harvest location.
Linked stockpiles would work, but I suspect your minecart solution is going to be rather inefficient:
- Unless you set harvesting to be performed by farmers only, harvesting jobs are taken up by the first dorf that happens to be free after the plant is ripe for harvest (with the exception of miners, who are intercepted on their way to their jobs and turned around to harvest). These dorfs will probably pick up the targeted plant, place it in your feeder stockpile, and then return to the fortress, passing by your target stockpile on their way to their next job.
- When the harvesting dorf has put the plant into the feeder stockpile a very low priority hauler job to move it into the mine cart is generated. Unless the harvester happens to be a dedicated hauler and you've got a fair bit of hauler unemployment, the harvester is likely to pick up a "real" job rather than the mine cart filler one, or a higher priority hauler one (mmm, old dry bones in the cavern: must haul to refuse stockpile immediately!).
- Unless you were lucky at the previous step, another dorf will trek to the feeder stockpile to move the plant to the mine cart. If you're lucky, that dorf may actually perform several plant move tasks while there (in particular if the only hauling jobs on offer are mine cart filling ones), but frequently it's going to be one plant being moved and then a trek back to take a higher priority hauling job.
Burrows might work (I've never tried to use them for things other than civilian alerts and procreation arrangements, but I fear cancellation spam).
Another alternative might be farmer only harvesting and have workshops close to the plots for the farmers to work in when not planting/harvesting. Workshops using the harvested plants might be an option. Of course, you'll then get a small number of dorfs trekking to the plant stockpile to pick up favorite food items, but that may be a better option (and you should be happy to get at least some dorfs who get something nice to eat).