The Buckingham saddles almost always have good ways to attach the saw. I don't remember if the ErgoLite has the brass snaphooks on both sides, but my Deluxe Master does. On this one, it has the snaphook, a small D ring and a large steel ring (1-1/2") all on the same webbing loop attachment. I cut the large rings off, and the snaphook on the left side off. Although I'm ambidexterous, the saws are all pretty much designed for right-handers, so I usually hang the saw on the right side. I have a small Petzl Caritool on the left side, and a large Caritool on the right. The large one will accept the handle of the bigger saws, and hold the weight. I use suspenders on the saddles. On the rear of the saddle, there is a webbing loop above the main structural webbing/belt and a small D ring below it. On this saddle, I clip my saw lanyard onto the small D ring. It will hold the weight of the saw, and keep it positioned behind you when you let the saw hang below you from the lanyard. Make sure the lanyard is long enough that the powerhead is just below your feet, the saws chain will tear you up if it hits you when dropped, running or not.
Pics of the Buckingham...
The following pics are of another saddle with homebrew mods for treework. On this one, I used a Kong Paddle on the right side to clip the saw into and you can see how I attach the saw lanyard/bungee to the rear belay loop. This technique will work on the Buckingham saddles, because nearly all of them have a loop on the back, in the center. It works fine whether the loop is above or below the main structural webbing belt, and will hold the weight of the bigger saws. Again, I use suspenders with this very lightweight harness to hold the weight of the saw. This one I use when I'm just setting anchors, pruning, or doing tower work on smaller towers. If this thing can hold the weight of a saw (with suspenders, anyway) then the ErgoLite most certainly will.
Hope this helps with your question about attaching the saw to the harness.