Hi Benn, Hi Ante,
Instead of having an "off" period between lit bulbs, add a simple diode OR gate for pairs of LED outputs. So LED outputs 0 and 1 each have a diode to the 1st triac's gate, LED outputs 2 and 3 each have a diode to the 2nd triac's gate, etc. Then the bulbs will step smoothly around and around.
A roulette wheel is good application for those extremely bright Lumileds. Use all 10 outputs then you just need DC and Mosfets instead of triacs.