I have never used sweetgum on a furniture project, but based on your work it certainly has beautiful colors and grain! In my youth, I split (axe, wedges, and sledge hammer) a lot of gum for firewood and it was a beast to split.
If it's quartersawn it's very stable. This stack has been in my shop for the better part of 3 years.... It varies from roughly 1/8 to 1/4 thick. Dead nuts flat after all this time.
We had 4 trees cut form our driveway area 14-20 inch logs. Tool them to a bandsaw mill guy and had them slabbed. Air dried for about 18 mos.. Blessed to have a big have a big ol Moak joiner.