Can't quite picture what you're doing from the description. Could you draw a simple picture and indicate what you intend to produce? Take a picture with your cell phone and post it. You can just use arrows to point to what you want to wind up with.
In general I always prefer to use a router table whenever possible. Putting a roundover on the four 4x4 legs would be easy, although I'd keep what I assume will be the four legs, as square as possible for the ply to mount against. 4x4 is also pretty heavy for a kitchen, perhaps you could cut a taper so the legs thin out toward the floor. This sounds like a very practical table. I'd seriously consider gluing up some hard wood to make the top. Finish the top with food friendly oil. It will look really nice that way. The appearance of this table will depend a loton your lumber selection. Look for pretty tight grain, and consider checking out Oak for the legs. Some stores have this kind of material in their stair making area.
Reading your post over again, I think you're planning to use 1x4 to fashion the legs. If so you can still taper the material, then glue two pieces together to make the legs. Then use some hefty quarter round on the inside joint of each leg, which will add strength and a more finished look. Extend the quarter round straiht up and fasten it to the table sides.
Once you get the legs together, use a rounhdover on the legs. Glue and clamp carefully so the two parts of each leg don't have any gaps. I don't think I'd want the legs splayed out, just straight down.
Hope I read this right.
Hope this is helpful.
The more I do, the less I accomplish.
Last edited by DesertRatTom; 06-21-2018 at 08:58 PM.