Damper and air flow/smoke

[Embe]

I have a residential prefab wood fireplace and some smoke comes into the house. The unit is about 20 years old. We use it for wood and it gets cleaned regularly, and generally works well. It also has a gas starter built in. It appears to be made by the Superior Fireplace Company and I found the Installation Manual on the web (Models RD-3300A, 3800A, 4300A; (broken link removed)). I wanted to improve the flow of air up the flu and looked at the damper and saw that whereas the smoke can go straight up the flue towards the back of the firebox, it appeared to obstruct smoke that is towards the front. It is designed this way. I have attached 2 photos from another fireplace in the house, one from behind the damper which goes right up the chimney, and one from the anterior of the firebox. You can see that the anterior firebox has only a tiny opening.

I removed the damper unit and there is no improvement in smoke control. In addition to the damper itself, there is a 5" Lintel Extension across the top opening that came down with the damper unit, such that when removing the damper unit, the overall opening is larger. I have attached photos of the damper assembly unit.

Should I remove the damper from the Lintel Extension and then bolt the shield in place?

What else do you suggest?

Thanks.