No matter what video processing the DVD player offers, the source material on the disc is already 480i/60 (30 frames per second, interlaced). That is inherent in the DVD format - there's no way around it.

I mean original film frames (of which there were 24 per second before the film was transferred to video). In other words, the player is working backwards to piece those original frames back together while taking into account the "p24"-to-"i60" conversion process that took place during the DVD mastering process.

This is exactly why deinterlacing is hard, and why "cadence" based deinterlacers often have better luck. Deinterlacing has to be done differently for sources that were originally 24fps film or 30fps interlaced video. After all, if the DVD is taken from a TV show that was shot on video tape, there was never a 3:2 pulldown performed and the deinterlacing simply needs to combine every two interlaced frames - doing a 3:2 pulldown as part of the deinterlacing process would actually mess things up. A flag-based deinterlacer trusts the person who mastered the disc to flag the video data properly ("this is taken from film" or "this is taken from video"), and if the flags are set wrong the deinterlacer is out of luck. A cadence-based deinterlacer looks at the patterns of the individual interlaced frames and tries to recognize when a 24-to-30 conversion (3:2 pulldown) has taken place in the creation of that video transfer, then behaves accordingly.