Mark has sent a solution to the Buzzy Bee problem. Here is the completed honeycomb with Mark's numbers in blue:

Ginny sent in the following:

My seven-year-old grandson Jack loved solving this puzzle.  I said I'd send it to you.  We are in America.
 

Jack's mum made a video for me as he doesn't live with me.
I can tell you that he started with the number 4 between the 3 and the 5 because he saw that pattern.  With discussion, he saw the relationship between the 4 and the 6 below and was super excited.

There's a video here with Jack saying a few things about his solution: Buzzy Bee.mp4 

Thank you Jack for your very good work and explanation, and to Ginny for sending it in to us.