The short answer in No, you haven't missed anything obvious.
I'm familiar with your goal, having wanted to do the same my self. My belief is that Export as Catalog, and Import from Catalog do not permit file gender changes of any kind. If, on the other hand, you Import From Disk the files you have previously placed on your laptop or any other drive, you will have the option of converting a proprietary RAW file to DNG during the import to your desktop system. You will, however, loose the catalog work you have already done on those files unless you create in advance of that import, side car files.
I am not prepared to instruct you how those sidecar files need to be created within Lightroom, but the option does exist. Others here will know in detail I'm certain. I do belive you may forgo retaining the History States of your files, that is, I fear that only the current state is written in the sidecar file.
There is also the notion of using the Adobe DNG Converter after the Import from Catalog, but here again there will be a trick to retaining all your catalog work.
John Caldwell