There are a couple of things you can consider.
1) replacing the flue. Just hire a handyman and get the double insulted stainless steel kind. They come in 3' sections, and 18", which will do about anything. Even with a fire you can lay your hand on them. They have things that will work with your roof/wall/timble etc. You seem to be wanting to work with a certified yada, yada, and they will loose their license if they don't do EPA yada yada. Which is understandable you want well qualified people, and I don't blame you for that at all. Total cost for mine which runs on the outside and extra's 600.00. about 10 years ago.
However replacing a flue isn't rocket science. I put mine in, so I know it is easy to do.
2) we have a Dutchwest Convection Heater (with a catalytic converter) It's solid cast iron and weights about 400 lbs, and its one of the small ones. The catalytic converter is something you kick in once the firebox reaches a certain temp. We never use it. The converter sort of works like a damper, kick it in and it recirculates the smoke and burns it. So in essence we never use the damper, and use the vents on the heater to control the fire. We paid 900.00 for it some 15-20 years ago the same heater last I checked a couple of years ago was 1900.00.
3) even if you get a new heater the flue has to be replaced. Get the one above.
Hope that helps.