I've come across my fair share of saplings and baby trees while climbing and usually sling them with a basket hitch. But I got to thinking that I could very well end up taking a fall on a triaxly-loaded biner.
Serious tri-axial loading typically happens when the sling is juuuust long enough to go around the tree. A longer sling lets the ends meet at a lesser angle on the biner. So it sounds like either you're using 8 inch slings, or your definition of sapling is a lot different than mine. YMMV but if a 24" sling is just barely making it around the tree, it's likely a good strong piece of timber.