Open the old catalog first, then select the images you want to use in the new catalog. Press Control S (PC) or Command S(Mac) to save out the settings. Make sure 'Include Develop Settings in Metadata inside JPEG...' is set on the Catalog Settings (Metadata) Dialog.
Open the new catalog and import the files.
Not all settings get saved this way: Flags, Collections and Virtual Copies don't get saved.
Optionally, in the old catalog, export the files in a temporary catalog, then import the temporary catalog into the new catalog.
Thanks! I appreciate the advice.