One observation I had... I think that the game takes the console region into account when calculating the day/night cycle duration? Kinda seemed like it, but not sure. Well, keep in mind that you wait about another half a second on every screen transition in that version. (Did they add a lot more graphics compression just for that version, or what?) I suspect what's going on with the passage of time is that the day timer keeps running during the longer loading time during which you can't make progress. Just to satisfy some curiosity, I tested on emulator to try finding the minimum time it took for each time of day to change, and I came up with 40960 frames for midday, 10240 frames for dusk, 6400 frames for midnight, and 7936 frames for dawn, for a total of 65536, the 16-bit limit. I also notice that the helping hand in Dizzy's house disappears for another 417 frames every 8192 frames of idleness!
I think that skipping Dozy in itself saves barely any time, and it's not worth it either (at least with my route) It would be worth it on a route that brings Dora down on your first pass!
I don't know if you've seen my videos of speedrunning Fantastic Dizzy for CD32 at less than the recorded speed, but I remember one of the funnier little timesavers in the Genesis and Amiga versions is that on the shopkeeper and on Grand Dizzy's cauldron, standing on one particular pixel will make the game skip the throwing animations when you hand over the items. That might not help with buying the bean in real time with the time you might spend lining Dizzy up, but maybe it could pay off with multiple medicine ingredients on the cauldron.