I really like the umbrella frame modifiers with the Cheetah LIghts. They are light, compact when folded and easy to setup. I used a 30" octa for the testing. Plenty of light with the light about 6 feet from the subject. No diffusion panel although that only absorbs about 1/2 stop. If you have both diffusion panels in the 24" snap frame box they may be absorbing a stop or more of light. Also, remember that 1/1 in H mode is one stop less output that 1/1 in normal mode. So, you can get back 2 stops.
Maybe the best thing to do is start with the 5" reflector, see what you get and then see what modifiers you can use that have minimal impact. The 19" foldable octa is a very nice modifier as well.
As for power, try the AD/CL-360 at full power at the higher shutter speed. As I discuss in the article on my site, the longer flash duration at full power permits higher shutter speeds. I also confirmed that the AD/CL-180 also has a sufficiently long flash duration so the same thing works.