I'm working to repair the pictured round wooden table. It has a wood screw that's completely stripped out, in addition the center post has cracked:
My suggestion is to use increasingly-larger drill bits to widen the hole in the leg. For example, assuming you're starting with a 1/4" hole, work up to 5/16", 3/8", 7/16" and 1/2" bits, and you will end up with a 1/2" diameter hole. Keep your hose clamp on while doing this to keep the crack from widening.
Then, take a piece of 1/2" dowel of a good hardwook (oak or maple would work well). Or, use a plug cutter to make a 1/2" dia. plug of a suitable depth to fill your hole.
Glue the dowel/plug into the hole, redrill the hole for your threaded insert, and reinstall the insert. The plugs have the advantage that when you reinstall your insert, the threads of the insert are biting across the grain of the plug vs. splitting the long grain of the dowel.
I'm considering augmenting the hose clamp with two part epoxy, sawdust saturated with wood glue, or wood putty. What would you suggest?
I suggest this for closing up the crack: Drill a couple holes that cross the crack and epoxy in some dowel pegs. The pegs will act to bridge the gap and keep the crack from opening wider. You can also fill the crack with epoxy to help keep it together, but the dowel reinforcement will greatly strengthen the crack. See the image below.
The table top screws into the stud, and it's easy to put a lot of force on the connection and spin the stud in the hole.
I would consider trying to find a screw insert with a much longer part that threads into the post. You're applying a lot of force to a very small region with that short stud. Lengthening the insert portion that feeds into the post will greatly distribute the force to the rest of the post.