DIY barrel stove

So I’ve been browsing this site for a few months now and there’s is tons of fantastic information but I can’t seem to find a solution to my problem. I built a 45 gallon drum barrel stove, before I learned about rocket stoves of course. So I want to get this one going instead of a total redesign. It’s mounted horozontally in my garage in a corner away from all flammable. It’s a detached garage. I have a decent sized air inlet, about 4”x6”, my chimney is 6”. I can get a good hot fire burning but after about 30 minutes and the barrel reaching a steady temp of 600 at the hottest spot it starts to leak smoke out the fire loading door into the garage. It’s not well sealed but I get no smoke until it’s hot and when I open the door it billows out. Is this normal because the rest of the garage is so cold? It’s -25C in Alberta right now.

If you shut down the air inlet will it start pulling air through the unsealed door cracks and reverse the leakage?
How tall is the chimney...and how many bends are in it?
Could you install some door rope (cord) and simply seal the leak?
If you open the door does the flame and smoke leap out at you or does the fire pull more air and start flowing normally?

I didnt try shutting the air inlet to see if it would pull back in. The chimney is about 16' tall, it sticks above the peak of the garage 3-4'. There are two bends in the chimney, after it leaves the stove about 3' up there are two 90 degree bends and then its a straight shot through the roof. I cant install any cord seal in the door because it just sits flat when shut, there is no edge for the seal to go into, poor design on my part but this summer im going to make a new door. If i open the door the flames dont leap out but the smoke flows out steadily into the room. I will take some pictures tomorrow because i feel like there is a simple flaw in my design that i just cant see.

I ran the stove again this weekend to test your suggestions/questions. With the air inlet shut there is no more smoke leakage. Also when I open the door with the air inlet even partially shut the flames and smoke leap out at me. I’ll be redoing my door before I do anything else thanks again I knew it would be something simple. God thing the lid of the barrel comes off I can just throw another one on

90º bends are not recommended, especially two of them. This is a case where you need a teacher alongside to understand where the problems are. If you can post several photos that will help.

Just a couple thoughts:

is your chimney insulated?  Insulated inside the garage, and the outside portion?  If not, it may be cooling too much and slowing draft

can you remove the 90* bends and use 45*s instead?

So....
From your description, it would seem to me that your chimney is too restrictive.
For a comparison, the average pellet stove has a cup of mass burning, and gets by with a three inch pipe (7.39" cross sectional area) on the average less than 8' in length,
a hi dollar version may have up to two cups burning concurrently and a four inch stack, (12.73" cross sectional area (my Breckwell has cautions against more than 12' of stack because draft may overcome the damping effect of the draft booster and allow the fire to  burn out of design parameters)).
A small wood stove with a 2'x2'x2' fire box stuffed completely full would have the rough equivalent of 20 cups of pellets (once air voids due to surface irregularities are factored in) burning concurrently and uses a 6" pipe, (28.89" cross sectional area) these stoves tightly control the draft air and will often "woof" out the door when opened because there is more fuel than air to burn it, and the open door allows an immediate flash off of the unburnt fuel.
A large stove with a 3'x2'x2' firebox stuffed full has the rough equivalent of 35 / 40 cups  of pellets burning concurrently, an 8" pipe with a cross section of 50.02" will still "woof" if the door is suddenly opened and unlimited oxygen is supplied...but usually the draft is adequate to pull all the smoke up the chimney.
An open fireplace of the same dimensions as the large stove would have a clay liner (on the average ...your mason may vary!) 12"x16" with a cross section of 131".
A large Victorian era fireplace with a firebox 5' tall x 6' wide x5' deep adequate for roasting whole pigs, or suckling calfs would have a burning mass roughly the equivalent of 120 pounds of pellets burning concurrently and the chimney would have a cross sectional area approximately 3'x3' or 1296 square inches.

FWIW heat sent up the chimney is wasted labor my Breckwell with a 4" x 3' stack extracts all the heat out of the smoke column to the point where the outside of a double wall pipe stays cool to the touch, with a 10' stack it pulls the column through the heat exchangers faster than they can extract it and grows uncomfortably hot, 140 degrees on the outside of double wall pipe. It currently heats a 1600 sq ft  doublewide in North Idaho with 70's era insulation (read inadequate insulation!) comfortably (73 degrees) on the equivalent of one wheel barrow of wood a day (40 lbs (roughly $5.00, (or 15 minutes labor daily))).

Perhaps your redesign would benefit from a better heat exchange configuration and a smaller fire where your 6" stack, (with its restrictions!) would be adequate for the volume of the smoke column.