Thanks for the reply - I found the problem a short while after posting this (though I'd already been at it for a couple of hours).
I was getting a "limesurvey upload file not found" error, and it told me to check my permissions on the limesurvey/tmp/upload directory, but those weren't the issue.
My upload_max_filesize setting in PHP was the culprit - it was set to 2M. Adjusting this did the trick and let me run the large file.
Part of the confusion here also involved IIS, since our site runs on IIS - there is a setting there (maxRequestLength in the <httpRuntime> element) which has a default limit of 4M for file upload size. But it turned out PHP was the limiting factor here.