It's always the same - things always seem to happen at exactly the moment you don't need them!
You have several issues going on here, as I am sure you are aware.
Firstly, a diet of cracked corn and nothing else is most definitely not good for your girls - it is high calorie, low nutrition food. It is therefore probably not a surprise that Violet is eating eggs - she is looking for the nutrition that is lacking in her diet. (It can also cause chickens to pick and eat feathers.) It is a very bad habit to get in to, so you need to start giving them better feed asap.
If you are going to have to wait for the chicken feed to arrive, then give them some other type of food. One very good thing would be scrambled or boiled eggs - as long as they aren't raw, it won't encourage egg eating. At least one egg per bird per day, two if you have enough. You can also give them porridge oats - made into a warm mash with hot milk or water - yogurt, cottage cheese (or other higher fat cheeses but in small quantities), and virtually all vegetable peelings (boiled for a couple of minutes to cook them through) and other kitchen scraps, leftovers from meals etc. You can give your chickens almost anything you would eat yourself, as long as it isn't too high in sugar or salt. You can also give them meat trimmings (cooked and cut into very small pieces), and cat or dog food (if it's dry then moisten it with hot water). Neither of these last two are long term suggestions, but for a few days it will help to give them a more balanced diet until your layer feed arrives.
Once you sort out the feed situation you may well find that Violet stops eating eggs. However, until then you need to try and remove eggs as soon after they are laid as you can, to remove the temptation as quickly as possible.
You also need to try and raise the feed bowls somehow - fixed to the wire of the cage, or on top of flowerpots - something to keep the poop out of them.
To introduce the girls back to the coop I would be inclined to place their open cage inside the coop (if you have space), or if that isn't possible then next to the open door of the coop, with a makeshift 'corridor' to give them access to it. (I have used pieces of fencing, clothes airers, cardboard etc. in the past!) Then they can decide where they want to be during the day, and in the evening you can see if they choose to sleep in the coop or to go back to the cage. If they are back in the cage, bring them back inside for the night, then let them out again tomorrow. As long as you haven't been heating the garage where you've been keeping them then they should still be quite cold hardy.
It is a shame you are allergic to pine shavings (not an allergy I've come across before!) but there are several equally good alternatives available - if you research bedding online then you may be able to find some suggestions for something within your budget and easily available online or in your area.