I can't quite picture what the gap is. The koolaid is dumped in but separate? Sorry, I've never made these and can't get my brain around it.
Kathy

Playdough-

Here is a link that might be useful: jar gift- Playdough

The jar will be decorated with fabric, ribbon, flowers. something!

Rip a piece of coordinating fabric and tie it in a knot or a bow just below the jar lid to disguise the gap and decorate the jar. Tie the instructions for mixing to the fabric.

Or cut a large circle of fabric and cover the whole lid and tie it with a piece of jute or sisal or cording. Leave an inch or 2 of excess fabric to make a "collar" and that will disguise the gap, too.

I'm worried about people picking them up, turning it on it's side, and things "shifting".

Then I think you'll need to increase your portions until the jar is full.

I decided to use some saran wrap- worked pretty good- I'm using the white tops for the canning jars, with a wide strip of fabric around the jar to match the color of the playdough.
Almost forgot the cream of tartar- wonder if it makes that much of a difference?