Ok, Brisbane Arborist. I'm a relatively new guy to climbing, maybe 2 to 3 years of sporadic climbing. I own an older version of the TreeMotion saddle. I still don't fully understand how some guys are able to fit their harnesses so that they're able to safely go inverted. It took me awhile to figure out how to get my climbing systems configured in a way that kept my attachment to the rope arranged so that it was always above me, and tending to be forced down into the saddle. A few times I had the kind of dangerous slippage out of the harness that you are referring to.
I looked at the suspenders offered by the folks that made the saddle, but it was relatively expensive, and did not get good reviews, if I recall correctly. My harness was not rated to support the weight of a climber inverted on those suspenders, I don't think. They were mostly intended to take weight off the harness and put it onto your shoulders.
To save money, and just because I didn't like the look of the "official" ones, I used a set of work suspenders that were pretty beefy.
They would not hold my full weight from dropping if inverted, but what they do manage is to try to pull the harness towards my backside, so that I pull out of the harness less easily than I used to, on those occasions when I find it necessary to try to stretch and reach downward for some reason. Usually after I right myself I'll grab my side "D's" and pull the saddle back up to make sure I'm seated in it deeply.
My suspenders have a single leg down the backside, and split into a "Y" just above the shoulder blades, I think. I like to bring the two legs of the"Y" up over my shoulders and then cross them in front. This prevents the straps from accidentally rolling off of my shoulders. It squeezes my neck a bit, however, when I'm first loading up with gear, but haven't put all my weight into the climbing systems yet. Once all of the weight of the harness is supported by the climbing systems, pressure on the neck is relieved.
In looking at photographs of your harness on TreeStuff.com, it appears to me that you might have a strong piece of webbing strap passing through the back of your harness, which you could attach to. On the front you have your "D" rings. You might be able to fashion your own suspenders out of webbing strap or even friction hitch cordage. The big question is whether or not you would trust that webbing strap material running through the backside of your harness.
That's all I have for now. Best of luck to you in this endeavor.
Tim