How to import 16 fps videos without frame duplication in Final Cut Pro?

I have a bunch of clips that are 16 frames per second. When I drag them into a final cut timeline, the system duplicates frames to create 60 fps.

Once this is done, rate conform does not work. It sees a bunch of identical frames, and only smooths between the ones that have changed. 24-to-60 works fine, but 16-to 60 is stutters.

I've managed a convoluted workaround using quicktime player and mass renaming stills in the finder. I can then slow the file back down and get the correct speed, and smooth motion. But doing this is very time consuming, and probably reduces video quality. So I need either:

A fix to final cut so that 16 fps files are imported without frame repeats.

or

Some easy way to relabel a 16 fps video as 24 fps, without actually recompressing the file - just speeding it up. (The files don't have sound.)

[Re-Titled by Moderator]