Without digging into too many details, I believe that there is a serious mismatch between the two heat sources, and they should probably not be mixed.
1. Most stoves have a lower heat rating than a house furnace. I'd guess 35,000 btu to perhaps as high as 60k. Most home furnaces have 60k to 120k btu output. The difference, of course, is that furnaces run only intermittantly, and their air flow is generally much higher. The largest stove in quadrafire's lineup comes in at 72k btu. https://www.quadrafire.com/products/5700-step-top-wood-stove
Their smallest fireplace insert comes in at 37,000 BTU.
2. In light of #1, you should expect a serious mismatch in what is called the temperature rise. Wood stoves are engineered around keeping the firebox hot, and producing a steady (but low volume of air) stream of continuous heat. Turning a high capacity air handling system loose on a low air volume system is going to guarantee a lower temperature rise, as the firebox of the stove was never engineered to lose that much heat to high air flow.
3. You need to measure the temperature rise of each heating source, not the final output. Measure the temperature of the air going in, and then the air coming out. This is the temperature rise, and it will tell you a lot about how each device is working, especially if you can figure out how to...
4. Measure the air volume moved through each heat exchanger. Get a cheap spirometer and measure the air flow. Then multiply by the duct diameter coming out. With a little bit of math, you can figure out whether your devices are really producing enough heat for the house. Kinda complex, but anything less is just guesswork.
5. 140° exhaust temperature would be WAY too high for a conventional forced air furnace. You would be at risk of burning up the heat exchanger from inadequate cooling, and that much heat going through the ducts would be kind of dangerous, as well. Most people signal acute pain at temperatures above 120°, tissue damage occurs at 140° and up.
6. Any draft problems you might have will not probably influence the air temperature rise, except that a fire not making enough heat won't have a significant temperature rise. If the furnace and wood stove share a common exhaust up the same chimney pipe, I would expect any fireplace to burn a bit cooler when the furnace fires up. That might be causing a bit of back-pressure on the stove exhaust, with a subsequent reduction in heat.
7. You should avoid any scenario where the stove feeds warmed air into the furnace. Remember my remarks about temperature rise? When all other factors remain the same, feeding warm air into the furnace heat exchanger causes it to run hotter, and it's lifetime is thereby made shorter.
8. Any reduction in air flow over the furnace's heat exchanger will cause the same problem: hotter air, shorter lifespan, with the production of holes that leak CO2 and carbon monoxide into the house. This is always a bad result.
9. If you are having heating problems in general for a system that formerly worked, check all your ducts for having adequate air flow. In my experience, ductwork never gets any better than the day it was installed, so find any problems. Really dirty vanes on the blower are the most likely source of low air flow, providing that you at least don't have an obstructed air filter.
10. I can easily imagine that the air passages of a wood stove could become lined with ash, dust, or rust, and then the temperature rise will be too low, regardless of how well the wood fire is producing heat. Clean if possible!