Several points:

1) I'm surprised the grass didn't heat up. I suppose it was very dry and brown? If it was still green, you were taking a chance.

2) It is difficult to maintain proper moisture in a plastic bin with no drainage holes.

3) Shredded newspaper by itself does not make very good bedding because it tends to clump. Some people do use it with success. If you are able to shred cardboard, that would be a great addition to the bedding. Cardboard is less likely to clump, and it makes castings with good texture.

4) The bedding will shrink. That is part of the process.

5) 4 to 5 times a week is a lot to feed them, unless you are feeding small amounts at one time. From what you describe, you are probably doing OK.

6) The bedding is part of what becomes castings. If you want a lot of castings, you need to have a lot of bedding,

What I would do:

Continue to add bedding. Keep the level of the bedding at 6 to 10 inches. Don't stop adding bedding until the bottom 6 to 8 inches is mostly castings. Stop adding bedding then, and let the worms finish it off. Then you can harvest. Or you can take the top couple of inches off and use it to start a new bin at that time.

Chevere, part of the point of the holes on the bottom of the bin is drainage, but another big part of it is letting air in. Worms don't directly eat the food, they eat the bacteria that eat the food. The bacteria need oxygen to grow. Closed bins (those without holes on the bottom) do work, but they're a lot slower than ventilated bins.

I had bins with 4 small holes in the corners that got stopped up so they let water out, but I doubt much air got through. I took a friend's advice and drilled 50 1/2" holes in the bottom and things have been much better.

I think that in a closed bin, the amount of oxygen for the bacteria is the rate limiting factor. I'm not sure what the rate limiting factor would be in open bins. Both bacteria and worms can grow in numbers exponentially, but I certainly haven't had that experience. I've gone from 1 to 4 bins in 1.5 years. Theory says it could be a lot more.

Hi Chevere,
You didn't say how many worms you have in your bin. I'm assuming as you're just starting out you probably don't have much more than a couple of pounds?
You have a large surface area,- 5sq foot, so although you don't have airholes in the bottom, if you keep the depth of material under about 4 inches you should get along okay.(this mimics what the worms have in the wild) I'd repeat what the others say above about adding bedding as needed, but you might also consider reducing the area of the bin by dividing it in two with a grill or something the worms can get through. If you only feed one half for the first couple of months, you can then harvest your vermicompost more easily by stopping feeding that half, feed the other side, and in a few weeks most of the worms will migrate across to the new food source.
As to feeding, worms will not eat more than 2-3 times their weight per week-(and this is an optimistic maximum, in most new bins it is considerably less than this). You can divide between a few feedings, or feed once a week. cover the food with fresh, moist bedding, and try to leave them alone! Dont feed again till most of the old feed is gone. Don't mix the food through the bedding, especially in a closed bin, as the decomposing food uses up oxygen, and your worms will want to get out of there.