Do I need to convert 60fps to 30fps so it will be reproducible?
You're not back to 60fps, you're still at 30fps but with every other frame discarded (or blended, or interlaced, depending on how the speedup is accomplished). 

When you discard every other frame, you're trading off temporal resolution. If you interlace, you're trading off spatial resolution.

Either way, if this appears smoother, something's wrong with the way the 60fps is being presented. Your playback system may not be able to keep up with the data rate or frame rate. If 1080/30 looks OK, then it's probably not a data rate issue.