This may make some people upset, but I will tell you right now that you actually do have time to eat on shift. When I was a first year resident, I would work a 12 hr shift never stopping to eat, and I would feel terrible by the end. Eventually an enlightened attending pulled me aside and told me every shift has at least one 5-10 min pause in it where you have time to eat. He told me that if I couldn't find those times, then I was doing something wrong. He was a wise man and it changed my perspective. I started finding those spots and eating meals I had prepped at home and would microwave at work. I felt much better/happier on shift as a result. That was almost 10 years ago and I still prep a lot of my meals (usually some type of meat, veggie +- a grain with some sauce) or just have the hospital deliver my meal. Their room service is available to us for free and pretty decent: steak, pizza, quesadilla, salmon, stir fry, etc.
I'm at a shop where our group sees 2.5-3.0 pph plus we see all of the Midlevel patients as well (usually another 1.5-2 pph) with an overall admit rate of 20-25%. So our pace and acuity is on the upper end of everything I see posted here and elsewhere. We all eat real food on shift and you should too.