One issue we encounter when applying this gap fix is the messed up UV distribution, but don’t worry, here comes the hot fix 
(as you can see, it stretches and squashes due to the geometry)
Set these 3 paramters like this.
And remember to tick on
Enable Per Particle UOveride
See the magic!

Now it’s uniform, even though the geo is a mess.
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You don’t need to recalculate the distance traveled which involves division by vector length. Not that it would kill performance, it just can be avoided in this case.
Instead you can subtract Emitter.DistanceTraveled by Particles.BirthDistance and get the same result.
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There’s an issue when the actor moves really fast and the distancetraveled is not registered correctly. Which, I need to to recalculate the distance again. It only works in your case because the actor move at a steady speed.
I’ve tested your method.
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You are right. I have only realized the faster and/or unsteady movement can drastically destabilize the U distribution. Interestingly, disabling “interpolated spawning” in emitter properties can stabilize the overall U distribution, but the “attached” portion of the ribbon head would suffer incorrect U distribution.
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