I feel like the design space here is as narrow, or narrower, than that for the Terminal Silver contest. Mainly because the prototypical card--Lab--has been the card against which other $5s are measured (better or worse) for a long time. It'll be hard to make one not overpowered I think.
I have a suspicion that a lot of submissions will be sharing design space with Wishing Well and Menagerie.
That said, it's not like there isn't any room for more powerful Lab variants that are more expensive. After all, Alchemist exists. What would you pay for a vanilla +3 Cards, +1 Action? Is that fundamentally unworkable as a card? Is there really no tweak that could be made that gives it a good price point?
"Draw up to " is not allowed.
But Minion isn't "Draw up to" it's "discard your hand, +4 cards".
As I see it, the distinction is that "draw X cards" always increases your hand size by the corresponding amount, as long as you have at least X cards in your deck. For this contest, X can be variable, but the card needs to, given enough cards in deck, always at least keep your hand at the same size, and at least sometimes increase your hand size.
Further, it must do so by drawing cards from the deck (and not gain to deck before doing so): if all effects that functionally just gain to hand are ignored, the above must still be true.