Of course, you need mechanically handle the jumping ahead of the minutes and seconds arms.
What you get tends to look like a very precise chronometer, the type a Mars scientist would wear.
Any mechanical design where units are not cleanly divisible would have to devise a way for the arms to "fast forward" over the gap and accept nonsensical results for a few seconds before midnight.
I can't see how that solution is superior to fast forwarding just the much lighter and already mobile minutes arm, but perhaps I'm missing something.
I don't personally agree that it would be a usability problem - people already use wrist watches which aren't perpetually oriented up, they naturally find the zero point and understand the position of the hands relative to it. The only difference is that the zero point for the minutes will not generally be the same as the zero point for the hours. I certainly don't buy the "it's not the UI we're used to so it is a worse UI" argument. Mechanically, incrementing the marks is much simpler - I'm not even sure how you would get jumping the minute hand forward to work normally nonetheless how you would handle things like adjustments; but for moving the marks it's just another gear, which most clocks would have anyways for incrementing days. I don't think reading the time for the brief moment when the marks are in motion (and thus you know it's precisely martian-midnight) is really any issue; the only edge case I can imagine is a back to the future type situation where you are trying to determine a specific time by looking at a stopped clock (or more likely a still photo of a clock) and can't see that it is in motion, but the confusion would go away immediately when you see the hour hand pointed at the zero position.
I'm not yet entirely sold on the moving dial principle, I've placed my wristwatch upside down on my hand and trying to read it gave me a headache. The angle the hands make with the line of sight is indeed not very relevant, but their relative position to the fixed known elements of the dial feels essential.