I like the spider theme of drow. IMO the problem is not that the drow are too much like spiders, but that they are not enough like spiders.
First of all, they are too sociable. It requires a suspension of disbelief that drow could work together without killing each other. Solution: make drow loners, coming together only to mate (and that infrequently, not more often than every couple of years. Or decades, even.)
They are also too active. I think they should be like spiders in the center of their web. Quiescent and torpid most of the time, but ready to spring into action when prey comes near.
My implementation would be based on demonic influence and lots of drugs. The drow have special powers because they sold their souls long ago to demons. They spend most of their time in drug-induced reverie, but can fight as if on speed. Drugs and demons make them pretty psychotic and spaced out.
The mushrooms that the drow eat are hallucinogenic, and low on nutrients. To conserve energy the drow don't do much. But when they do move, they are deadly. Their magical powers enable them to gradually dream their surroundings into existence. They don't have to worry about how to get equipment or wealth or actually set up a functioning economy; stuff just gradually congeals around them after years of dreaming.
You could have cities of drow, but they would be like ghost-towns, holding maybe 1% the population of an equivalent human city. And any particular drow would be doing nothing 99% of the time.
Some drow might be exceptions to these general guidelines. They are like the kind of spiders that actively hunt their prey instead of waiting in their webs. These might have all sorts of crazy motivations, including building up armies and crushing all surface races, and might cooperate with similarly obsessed drow. "Drug crazed and demon possessed" would still be the predominant themes, though.
Some good stuff...
To add a little more flavor when I use drow as villains in my campaigns, I do make them more spider-like..or at least, one particular subculture of them.
This subculture sees Llolth more like a black widow spider than she is normally depicted... Her avatar to them resembles an almost Shelob-esque "Red Widow" drider, and she is much more bloodthirsty. As a consequence, the females of this subculture are cannibalistic carnivores, and males are a rare commodity. Only those males with exceptional abilities ever get to reproduce- the rest are thralls, and eventually, meals. Males are almost never seen by surface-worlders unless they enter one of their cities. Within this subculture, Drider-hood is a mark of Llolths favor, not her displeasure - her priestesses actively request this transformation, as do many of their culture's heroes...and Lloth indulges them. Among THIS subculture, the Driders are not sterile, either.
They are very powerful, but because of their societal practices, they are even fewer in number than their kin- too few to be a serious threat to the surface world. However, because their driders reproduce, they are growing in numbers very quickly...