This is a good question. A color changing LED in a single package (different from an RGB LED) is actually multiple LED elements, I think red and green usually) an are controlled by tiny integrated circuit embedded into the LED to control the time delay between transitioning the various colors, that's about all I know so bumping for the makers response.

Yes, although the colors you defined could not be made from a doping process with consistency. it would be more ice blue to red or pink, and a minimum
of 10,000 units plus prototype time and cost.

Not a good ROI to see it happen.

You could take an RGB strip, and force this to a degree from a remote control version, and shorten the length, that might be the easiest or hack into one
and see what you can achieve.
2 blinking bulbs, with custom colored caps side by side, could be handmade too, but I doubt youd see low cost mass production due to demand.

I think its a good idea.

Maybe youll find something in a toy, or retail product you can adapt, or build on your own.

Getting a new product in production, regardless of what is, ultimately takes longer and costs more than expected, that only changes with volume.
Order 100,000+ and it gets done cheap and fast.