Here is my suggestion it should work in theory but I haven't tried it yet. If you have access to a development server try there first.
Configure things so only you can access the 3.1.1 sites (prevents any changes to the DB other than you). If you have access to the IIS config you could add a 'secret' portal alias and configure each IIS site to only respond to this alias using host headers.
Back up both the source and target databases so you can put things back if things go kaput
Update the 3.1.1 sites to 4.4.1 so all are working on the same version. And make sure they are working at the new version.
Make sure the target install has all the required modules installed.
If the sites to be exported are using 'host' skins make sure these are installed on the target install.
Export the newly minted 4.4.1 sites including the content. (note If you have any modules that don't support exporting/importing then these won't be in the package)
Export the users from each site using something like Bulk Reg (http://tinyurl.com/3a4qqf links to Snowcovered)
Import the site into the target 4.4.1 install
Import the users into the newly created site.
Cross fingers Take deep breath and check how things went. At worst you should have at least the framework of of the sites moved over so it will reduce the time required to manually recreate them if necessary.
Post back here on how you go then others (and me!) know if the above will work.
HTH
Antony