If you want to maintain grass paths with minimal invasiveness, the best method is to trench around the beds. Make a 6" vertical cut straight down through the sod, then create a flat surface exactly the width of your favorite hoe at the bottom of that cut, then build your growing bed inside that perimeter. You will still have issues with the beds drying faster, but less so than with raised beds. You may also want to consider slightly narrower growing beds, because at 48" reaching over the trench makes it difficult for some to harvest the middle, and standing in the trench is more likely to result in a painful turned ankle. The grass will still try to invade, but a quick weekly shallow swipe with a sharp hoe will easily keep it in check. I use grass paths, but my beds are 30" wide and up to 120' long, in groups of six, so I greatly reduce the perimeter maintenance because I don't have to do as much edge work as your design will require, with grass between every bed. Alternatively, you can install some type of physical barrier, but it should be at least 12" deep - many lawn species will easily send roots below that level in search of fertile soil.

The predominate grass species around my gardens is Quack Grass, which spreads via rhizomes that can go quite deep into the soil to find new territory to grow in. Eventually I found that 10 inch Aluminum Flashing, inserted vertically into the soil at the bed perimeter, was the best way tp keep those rhizomes out of the beds. Janet Macunovich, in her "Caring for Perennials" talks about using plastic Carpet Runner as a barrier doing much the same thing I do with the flashing.