We had a great K year because we had a great teacher. Here are a few easy things she did to make it fun for the high levels.
Hopefully you can suggest some of these ideas to your teacher, if you think they would be good a good fit.

When the children were practicing writing letters, she would quietly suggest to the higher level kids the idea to see how many, or the longest, words they could write that begin with that letter. And for sight word practice she would give them chances to write words that rhyme with the word. When they moved to sentence writing she would challenge them to edit their work and make a longer more detailed sentence.

For the students would get done fast on the craft/scissor projects, she would have them write as many detail words they could think of to describe the craft. I.e.. fuzzy, brown, sticky

She did similar stuff when doing math & numbers, many times my child had more work done on the back of her paper than on the front because she was given the option to do the easy, the hard, or both. ex. On an addition facts worksheet, she would be given the choice to keep doubling the answers on the back and see how high she could go. My DD loves a challenge!

The children were never forced to do the harder things but they were always given the opportunity, which is important.
Another plus was that we were free to substitute or alter homework as long as we kept to the subject area and basic idea for the task.

Differentiation should be mandatory in every class, and especially in K, because it has the widest range of levels. Some kids don't know their letters while others can read and spell.
All it takes is a little bit creativity and most basic assignments can be tweaked for the more advanced student.

I think the biggest problem is that many people believe that K is supposed to be fun, but they don't realize that the word "fun" to our kids, means to actually use their brain!

I wish you luck and send lots of hugs to those of you who are suffering!