If they allow interlaced entries, then you could apply a soft telecine to your encode. In the command line tab, add in the Custom x264 commands:
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--pic-struct --pulldown 32
Otherwise you don't have much of a choice. Your best option is assuming your footage as 29.97 and re-editing your video at 29.97 for the smoothest output.
Sure you can use changefps or convertfps on your finished video, but one's gonna add duplicate frames that will hit on smoothness and could possibly be detrimental to sync, the other's going to introduce a lot of blending which hardly is a good idea.