I am guessing you are using briquettes?
How large is the basket? Around and tall?
How far off the bottom of the drum is it?
If the gap around the lid is not giant it would probably be all right. You may just have to close the lid vent a tiny bit.
When I light my drums, which one has a 16" by 12" tall basket and the other is only 6" tall. I fill um up and use the weed burner to light one side of the lump coal.
It really sounds like you have a problem with the basket and the coals more so then air sneaking in the lid.
When I light mine I let the temp hit 180 and close one of the two caps. 200 and I close the second cap. If the temp does not rise to 225 then I close the ball valve a tiny bit and take one of the caps back off. Actually one cap off is more airflow then one ball valve open. I did scroll and look at the pic in the first post but its hard to see. Any chance you can post us a few more pics so we can see what you are working with?
Don't give up.
We have the technology to help ya fix it.