I had a moment to play around with my HQV equipped Denon 602CI which can output 1080p24 and the Sharp was able to accept the signal. Running through the HQV test disc I noticed that with the latest firmware, Film Mode Standard was the one with the least amount of artifacts in the moving test patterns. On actual footage Film mode Advanced High/Low looked very clear with lots of detail. Film mode standard looked like the best compromise to me since it avoids the soap opera look. Film Mode off had quite a bit of artitfacts on the moving test pattern as well.
... Aquomotion was set to 120 High and I was testing in User mode.
Even though Film Mode OFF did not do as well on the HQV moving test pattern, I've been using it for the most part this weekend and it appears to do the trick for 24P playback. It does not have the typical smooth motion look and appears to be a good option for those looking for 24P playback from 835 series.