I need a quad NOR gate that is pinned out like a quad AND gate? Is there a good way to search for this?
I doubt any such database exists (finding it and searching it sounds like a lot of work), but if you (skillfully) do a parametric search, there are very few families to search in so it only takes a couple minutes to scan the few pages of part numbers. 

The 74xx02 series is not what you want

The 4001 series is not what you want 

The (ancient and probably unavailable in TSSOP) 74XX33 is not what you want  

The 74HCT7002 looks like what you want if you don't mind ST inputs, HCT family.