I would not hop for lunch and then go back to DHS. That gets very time consuming in my book. Now if you are talking about enjoying DHS for the day, then going over to Epcot for a meal and then staying there, that is different.
I like to park hop, but not to just eat if that makes sense.
If you really want to leave Studios just to eat, I suggest eating in the Boardwalk area (ESPN and Big River Grille are both tasty for lunch) or to one of the resort restaurants at Beach Club or Yacht Club. Any of those would be closer to Studios and also not involve the whole issue of getting into Epcot through a bag check and turnstile.
I know DHS isn't known for its dining, however there is enough there to find something for lunch. We enjoy Pizza Planet, Fairfax Fare (enjoy their salad and dh likes their bbq okay) and we love Sci Fi and Prime Time for a full serve meal. In my opinion the food at DHS is not so bad I have to go outside the park to eat. I may not make a special trip there just to dine like I do at Epcot but I find the food at DHS about as good as MK and AK.