I think cucumbers are always better off growing up a fence or trellis and off the ground.
That is a great picture Kim, with the grill in the middle of a sea of flowers.
Natalie, since you have to pot up your daylilies anyway in order to movce them maybe you can leave them in the pots and put your veggies in the fenced in area. Then you can make new beds during the summer for your daylilies. Maybe the dogs will keep the deer away!