I hate to toss a little more cold water on this idea, because roll out nest boxes are fantastic! I have them. But you specifically said you wanted to use the foam with a hole in it, with a funnel toward that middle where the eggs would roll down, and that you were concerned about the hens' comfort. If that opening is large enough for an egg, then it's large enough to trap a hen's leg. If her leg slips out from under her, she may well panic rather than simply pulling her leg out. For all she knows some critter has just grabbed her by the foot and she'll try her best to escape. So now instead of being comfortable she's injured, and will probably not go back to that nesting box when she recovers.
By the way, my girls are perfectly comfortable in their nesting boxes, which are slightly (and I emphasize slightly) tilted back. I don't have the ones where the eggs roll out the back, then roll back forward toward the front. Mine simply roll out of the nest into the exterior collection access. During the winter I closed the opening off and just gathered the eggs the old fashioned way.
And yes, if you have one egg already in there that you didn't get a chance to pick up yet, and another eggs plops out of the vending machine on top of it, you're going to have 2 cracked eggs. I hate telling folks who have put a lot of thought into a good idea that there are reasons why it probably won't work, doggone it! But I'd rather do that than see someone with a great imagination go through all the work expense of building something just to to find out that it's just not practical. I'm sorry.