I see no problem with your plan as far as the concrete work goes. Quick set is fine as long as you work fast enough. I don't think you'll need the mesh as long as you get some rebar in there and pin it to the existing slab.
As for the threshold, I'd let the concrete cure, then put your threshold in the opening. Before placing it, put a couple thick beads of silicone under the threshold and where the sides of it will meet. You can screw it down if you want using some tapcons.