Zoe's habit of "chewing on anything plastic" is dangerous. She could have some plastic piece lodged in her digestive tract which might be causing her to vomit.
Is there any way to remove those plastic things that Zoe is fond of chewing? I had a cat who loved to rip papers apart, and fortunately he didn't swallow the pieces. Still, I didn't want torn magazines and papers, so they were put in a cabinet. If Zoe is swallowing wads of paper that don't pass that could be causing her trouble as well.
As far as Zoe overeating when you go away, there are things you can do to control that. Take a look here: www.drsfostersmith.com
Type in for keyword: automatic feeders.
I've used these feeders for years with my cats. They also come with ice packs that you can insert under the dishes in the feeder to keep canned food fresh. I haven't used the automatic waterers, but there are many TCS members whose cats love them.
I agree with you that hunger is not why Zoe is chewing on non-food things. I'm assuming she's your only cat, and it sounds like you go away most weekends. It may be that she's bored and/or lonely. Bored kitties tend to get into trouble. If possible, have a friend or relative look in on her at least once per day while you're gone. Or, hire a pet sitter to come in once or twice a day. The fee is usually inexpensive for one kitty - maybe $10-15 per visit. It's a good idea since a lot can happen in 24-48 hours, either with your cat or your house/apt. It's peace of mind to have someone checking in to make sure Zoe's alright. A sitter can turn lights and radio on, make sure it's not too warm or cold, and most important, spend time with Zoe, playing or just cuddling.
A vet visit would be a wise thing at this point, since the vomiting is frequent, and she has a history of eating things she shouldn't. You should also mention the unusual fact that Zoe only vomits at night. Not to scare you, but I had a cat who did that - 4am every night. It turned out he had a very serious illness.
Hope you're able to get Zoe feeling better soon.