We lived in Hawaii for 24 years and have cooked many a pig in an imu like the one you have pictured. You can get the same taste by just not adding a lot of flavoring wood when smoking pork. The main difference you will find in flavor is from cooking large cuts (butt) and not the whole hog.
When we make Kalua Pig, I just take some pulled pork and add it. Tastes better than the imu variant in my opinion. Honestly, if you aren't at a luau, and order it in Hawaii, you will get pork made in a slow cooker or oven.
TL;DR Just smoke your pork without a lot of flavoring wood and you'll have an end product that beats most plate lunches you will find in Hawaii.