There are a couple of things i would try.
I would line the bottom with firebricks. You can call a brick yard in your area and probably buy seconds or thirds. Stack/arrange so they line the bottom and possibly extend up the side walls. They might lay side by side and curve up the walls.
This would create a smoke chamber below the grate. Lay a piece of plate metal on top.You can slide from end to end to experiment with while cooking. I would leave it unattached for future cleaning.Probably will work best slide to exhaust side.
Your grate would be above this.
Using the firebricks would help to maintain temps but also would allow you to move them and the hole of smoke entering the pit.
With the size of the pit, guessing 3 foot, the hole location will not change a lot(i think)Do you want a hot spot on the center of pit or the end of pit?
It looks like you are adding flanges to edges of door openings. That is a great idea.
Sealing up the pit will add to your smoking experiences.
Just my ideas. Hope they help,