Ok... I have had some illuminating, although annoying, results with continued testing.
I checked the map SFS files to see how the retail game handled water. What I found out is that the retail game actually only uses 16 frames in water animations as opposed to 32 like Carsmaster's water mod.
When I reduced animation length to 16, the "choppy" discontinuity disappeared. What is even more remarkable is that the smoothness of the water animation didn't really suffer from this.
Then, I checked out Carsmaster's animation frames a bit closer.
Turns out that frames #00 and #16 are identical, and the animation actually loops twice within the 32 frames supplied.
What I suspect is happening is that the game's water is hardcoded or otherwise set to only use 16 frames, even if more are available. With Carsmasters' animation, this was not a problem and no one noticed it because the animation itself contains the loop twice, once from #00 to #15 and the rest repeats the same sequence. So, when the first 16 frames repeat, it doesn't really change anything.
However, with my animation, it cut off in the middle (frame #15) and returned to the beginning (frame #00) without playing the important frames #16 to #31! This caused the animation to draw itself in an erratic manner. So, what I did is I dropped the odd numbered frames from the animation, and renamed the resulting frames logically from #00 to #15. The water now behaves normally and I shall upload a second test download soon.
Addendum: I have also discovered additional water texture animation called "Caustic", but GIMP refuses to open the TGA files. I'm downloading Photoshop trial version at the moment to see if it can open them.