I would suggest you add a smaller amount of hot coals into the basket first. Start with no more than 1/4 chimney...you may actually need even less than that...say 15-18 hot briquettes. Offsets are less efficient than a full vertical like a UDS, but a small initial fire should get the job done. Keep the hot coals together in one place, like the right front corner...you want a small fire that slowly spreads to other fuel as the original fuel is nearly burned out in order for the minion method to work best. Carefully fill the basket with cold briquettes so as to not disturb the hot coals, but cover them with cold briquettes. While loading cold briquettes, intermingle your wood chunks in layers throughout the basket, with one chunk in contact with the small fire-base you have to start with. Use the same number and size of chunks you normally would if you add during the smoke. If you place most of your smoke wood closer to the initial fire they will be used up sooner, so if you want longer smoke you need to mingle the chunks throughout the fuel. You may need to adjust your intake draft settings differently to get the same smoke chamber temperature. This should give a longer burn as you'll have less briquettes burning at one time from the start. The hot coals should slowly ignite the cold briquettes as the burn progresses and spreads. If too much intake draft is allowed you will likely experience smoke chamber high temps within an hour or two, and this is difficult to control, so start out low and slow until you figure out how much draft is enough to achieve your target temp.
It may not work for your application, but some guys fire their UDS or WSM by placing the fire in the center of the basket using hot coals into a metal can with both ends removed. Then, fill the basket with cold fuel and lift the can out. this allows the fire to spread in all directions, but a major difference here is the intake is down low and under the basket coming in from all directions instead of on the far side like yours is.
I have zero experience with your smoker, so don't know if the minion method will work well for it or not in a manner as I described. You may need to modify the method for firing and filling the basket to achieve the best compromise in temp control and length of burn. For example, instead of firing in the right front corner, maybe the right rear or left rear would work better...possibly the center/rear would be the best for the initial fire. It depends on where the draft inlets are located, and, where the fire-box exits into the smoke chamber. These two factors have a major influence on how the fire will react to draft flowing through the fire-box. If the fire spreads too rapidly, you may need to locate the hot coals farther away from the intake inlets so the heat of the fire isn't carried directly towards the unlit coals, but instead slightly away from, or around them. The flip-side would be the fire burning too cold and/or not spreading, requiring placement closer to the inlets. Hope that makes sense...but there are many tricks that can be incorporated into controlling the fire and smoke.
Again, you may need to play with the minion method a bit to find that sweet spot where the smoker and you are both happy. Shout back if you need more help figuring this out. Once you nail it down life in the smoke will be golden.
Don't feel bad about if it doesn't work the first time...I'm still mastering the minion method in my 26.75" Weber kettle, and I've been trying it off and on for about 10 months...but then I'm pretty darn finicky...LOL!!!