Lump charcoal being mismatched shapes tends not to pack in so tightly. And yeah, lump charcoal burns hotter and doesn't last as long, and with a lot less actual charcoal in the basket, it will burn out quicker. The advantage is way less ash and no chemical additives. This can be had in several brands of briquettes too if you pay attention to their labeling. If the lump is working out for you, I suggest trying some Royal Oak briquettes if you can find them.
If you are pulling out the basket and noticing you have unburned patches of charcoal, one thing you can do is to use firebricks to make an S shape of charcoal in the basket, forcing the charcoal to burn a better pattern and ensure it burns it all. Humprhey's makes some little metal dividers for the basket, you can see them on their website. Firebricks will do the same and can generally be found locally.
XL Big Green Egg, Weber kettles, WSM 22.5" and Pellet Pro adapter