Yes, deli cups are NOT ideal...they are too cramped & a snake will still feel exposed...there's no privacy, which is WHY I suggested a paper bag.
(Future reference: Don't heat the f/t pinkies...just thaw in cool water & pinch-damage the nose to release more scent.)
DO try a live one next...that's likely what she's looking for. And you can do one of 2 ways, to make sure she focuses on it: (1) either put her in a closed paper bag with it (a couple pin-holes for air, secure the top closed & leave bag in her tank over-night or until you hear the pinkie squeak to tell you she's eating...then IF you hear that, DO NOT DISTURB for at least 60 minutes...plenty of time for her to get it swallowed, otherwise if you barge in, she'll panic & spit it out & may refuse to eat it. Got that?) If you want, crumple half a paper towel to put in the bag too, just for a little traction & sense of security...she should have no trouble hunting the pinkie.
OR (2) put the live pinkie in a small flat bottom bowl (about 5-6" wide) that's too heavy for the snake to tip over, and leave the bowl in her cage overnight. It can help to put the bowl under her cool-side hide (take the paper stuffing out to make room). Your snake will feel braver being under cover, and braver by being able to look down on the pinkie in the bowl for a while while she gets up the nerve to pounce. The bowl should be deep enough (2") so the pinkie cannot escape...you don't want to need to search the cage for it.
Thaw pinkies IN cool water for about 10 minutes at most...they thaw fast. DO NOT let them sit out to thaw...they spoil that way. King snakes aren't known for caring much, but maybe you've got one that does care, especially since she's probably only had live so far.
Good plan on feeding live about 7 times before trying f/t & 2 pinks at one sitting. You'll get this...OK?