Ok, a couple of things. I love smart-ass Spidey, because that's classic Spidey. It's Spidey as he should be.
Second the thing is, Gwen is a scientist, and, given the information they had and the results they were getting with their own experiments, Gwen likely viewed Pete as a fluke. There is simply no way, given the information they had and the trials they were going through with their splicing, that Pete should have lived, let alone gotten the powers he did. She would be [I]very[/I] careful before trying to replicate it, even if she really desired to.
I could spoiler some more things, but I don't want to ruin movie 2 for you.
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Spec Ops continues to make you do horrible... horrible things.
It's not so much the spider itself as it is what you end up doing to it--first pincering a good number of its legs off, then almost drowning it, then even after you finally kill it, you have to rip off all its remaining legs and use its hairy body as a puzzle key. "Puzzle your way through some cold unfeeling factory" just can't compare, although like you said, pretty hard to follow up the spider and not disappoint, I think.
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The spiders were spliced by his father with the correct formula before he went missing. Connors didn't know that, so was extremely hesitant to do any human trials without knowing more. There is also some speculation that Pete was prepared in some way for this, either intentionally or unintentionally.
As for the super spoilery spoiler, Gwen Stacy is slated to die. Gotta make way for MJ, and it follows one of the early Spider-man plots for Gwen to get on the wrong end of one of his nemesis'.
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