As of now, given the constraints, you cannot achieve what you have set out for.
Firefox app would be able to restore bookmarks using these methods, in the absence of a hack:
- native settings option to import bookmarks. This is not available in Firefox for Android as of now.
- Using Web Extensions/ Addons. Firefox for Android doesn't provide API support for manipulating bookmarks as of now.
- Read and write to its browser.db database using a universally accessible content provider. Firefox's content provider for this is not accessibly by any user other than Firefox itself.
- Full participation in Android Backup Service. As a result, a user can use adb to backup and restore Firefox app's data. Sadly, Firefox explicitly disallows backup as of now, so adb is also out here.
- Using its own implementation of cloud backup service. It does provide a sync service -- but then, you don't want that so this is also not an option anymore.
- copy and then restore the browser.db or into your another phone. That database contains users' bookmarks. Alternatively, use a root backup/restore solution, such as Titanium Backup.
- Use content provider with root access to read and write into browser.db. But if you have root access, "1." is plain and easy.
As you can see from above, your options, as of now, are: get the devices rooted, or use Firefox's sync services.
Third option is to raise a feature request with Mozilla to provide bookmarks import, and extension support for manipulation of bookmarks.