I'd keep the park scene because it adds pertinent information to the film and the reveal is quite a clever shot.

I agree with you about the rest of the scenes though, in fact I'd go further and try to trim some of Newt and Burke's more cringe worthy lines (and screams in Newt's case).

I'd intercut the robotic guns with footage pulled from AVP2 to get past the cheapening re-use of Alien footage from other scenes in the film (frankly it's all AVP2 is any use for).

I don't know if anything can be done to lift the quality of the rear-projection work so it doesn't look quite as fake.