So because of how the tree was allowed to grow prior to purchase, I feel like I am pretty damn limited to how I can train it at this point. I was thinking that I could remove all but one branch and try to turn it into an informal upright, but have decided that I'd prefer a double trunk and could remove all but two of the branches. Thoughts?
The azalea pictured is still very young. There is nothing substantial enough to direct the style which means you can develop almost anything with it given enough time and patience.
For informal upright you will need to keep one branch and a leader. That won't leave much but good bonsai is often a case of stepping back to go forward.
Twin trunk should divide really close to the ground so if you want twin trunk you'd need to plant this one deep - right up to the cluster of branches. In a year there will be roots all round the trunk and from the branches close to the soil. You could remove unwanted branches with roots and grow new azaleas and just leave the best 2 for a twin trunk.
Broom will be much quicker and easier if you are happy with a skinny stick in pot broom style azalea.
The good thing about azalea is when they flower nobody bothers to look at the structure, just the flowers so you can get away with skinny, young trunks. Just trim all the long shoots as they grow over summer. Stop trimming at the end of summer so flower buds can set if you want to see spring flowers.