­Doomsday, trading being on-demand (without a sac outlet) and losing half of your life for +1 and on a death trigger. Might be too strong, but doomsday combos are pretty hard without Laboratory Maniac and Tendrils of Agony, so I think it's okay.

I think it's cool. Exiling your library as a drawback is already a drawback of such magnitude that losing life isn't really even necessary.

While you would lose some reference value perhaps (how much that matters for a core set is questionably), I would consider going for 4CMC, "... for four cards...", and making it a 4/4. It becomes easier to remember its effect precisely and hence it will stick out more - becoming indeed more memorable and iconic. 4 for/four (4) 4. 4 times 4. 444 or 4444.

Considering that Doomsday is traditionally a combo machine, I don't think that how large the creature exactly is even matters that much. If you wanna go for some crazy combo right off the bat, you should sac it asap anyway.

Well, my other plan for this was to have 5, 4, 3, 2, and 1 referenced in a minor change. Changing the P/T to 3/2, setting your life total to 1. But that might be too punishing and turns off all the "fun" Doomsday combos that use Gitaxian Probe.

That 'theme' seems like it would be way too elusive for hardly anyone to notice. It also doesn't help that much with how easy it is to remember. I call 'gimmicks' on it.