We don't use WeBWorK for regular exams/quizzes, but we do use it for gateway/skills testing. In that case we have the students work the entire test in WeBWorK, and have the luxury of having a lab in which students can work: then all students are sitting at a computer, and the system can manage the time limit. The lab is staffed by proctors whose job it is to monitor students' activities to ensure that they are not cheating.
This environment has the added benefit that we are able to set a firewall either on the computers or at the router that disallows connections to any site other than WeBWorK and our DNS/authentication servers. Thus we don't have to worry about students using something like WolframAlpha.
That said, I can't think of a good solution to the logistical issues you're facing.
Gavin