Basically, pausing during the game should be at least as informative as the preview.
Not displaying vital information during the game is bad. It's comparable to making the exit invisible and showing it only on the preview screen. I don't know any other game than Lemmings that shows the target once, then hides it permanently.
Watching other people play suggests that I'm not alone with forgetting (initial) and (required). Ichotolot has watched namida's live recordings, and namida goes back to the preview occasionally to read the numbers.
Making people remember numbers is a cognitive load that we cannot justify. Whenever we can remove mechanical thinking, it's a good thing to do. Then, we can focus on other things.
People are good at pattern recognition, not at remembering numbers. So let's allow them to do the joyful pattern recognition first, by looking at the level inside the game.
If an interface has problems, but there is no alternative program, people will use it anyway. And they will learn it, and learn to work around its shortcomings. Lemmings in the early 1990's was exactly such a program. :-)
Uncluttered GUI is a very strong argument in general. When an interface looks like an airplane cockpit, it's badly designed. With too many functions and statistics, you can't make a permanent button/display for everything. However, in the case at hand, we have 2 extremely vital numbers, not 5 rarely needed buttons.
I've always thought that you need 4 numbers for an adequate full-information display: (initial), (out+hatch), (saved), (required). Alone, (out) isn't too useful, either (out+hatch) or (initial-dead) seems better.
From your suggestion of (dead), I suspect there's a 3-number combo that works completely well: (dead), (maxdead = initial - required) and either one of (initial), (out+hatch), (initial - dead). The reasoning is that in singleplayer, we don't care about how many are saved exactly. We mostly care about how many we can still neglect. It remains important to know the initial count for general early-level planning.
Well, the contest levels are about saving a small amount. Here, we care about the exact number to save, not about the neglected. ;-) This type of level is not as common as save-79/80-levels.
-- Simon