Import fails to bring in widgets

I’m setting up a dev environment to update an old website. I first used All-in-one-WP-Migration to export the whole site, then imported it into the dev install of wordpress. All the sidebars were imported, but almost all of the widgets within them were missing. So, I then went to the old site and used Custom Sidebar’s export/import function, exported the sidebars then imported them into the dev site, and still almost all widgets didn’t come over. The sidebars are there, but they’re empty.

Any ideas why this would be and how to fix it? I have over 20 custom sidebars containing hundreds of widgets, so I really don’t want to have to do this manually each time I move from dev to main site or vice versa.