The stripe needs some time to get from 0 brightness to „full“ (255) brightness (Its better that they started directly full)
The transition time does not considered (may I would like to say is more like an disco, colors change very fast)
I would like to change the color over serval minutes (15 or more). Maybe a script is not the right way and an Scene or automation is the method of choice.
The transition number is for changing from the previous state to the new state. This does not affect the color loop at all. The reason why it takes so long to get to full brightness is you have brightness 255 with a transition so it is transition from the previous brightness to 255