You're gonna want to use Beowulf's EX moves to convert things into super as well as optimize combos. The enemy enters a sweep state after they exit Beowulf's grab for a second time; however, using EX Grendel Killa (it saves your OTG too) allows you to bypass that and continue the combo (if they're not at full undizzy; if they are, you can just super for some more damage).
Moonsault is a whole different thing. Usually you want to use supers if you catch both the opponent and their assist character, only if you aren't sure you can get a happy birthday and double snap off of it. It is also used to kill at the end of the combo. I wouldn't start a combo with it, personally, but it's up to you. Using 2 hype at the beginning of a combo kind of ruins any chance of you changing your mind to do some other set-up (although you still have 1 hype remaining granted you have 3 hype at the start, so it's not ALL over).
And speaking of style... doing a penguin at the end if you start with 3 hype isn't bad either. Funny enough, it is actually optimized. It allows you to kill the last opponent if their hp is below 1550 (times Beowulf's damage multiplier), which is more damage than any regular canis major will do, even at 0 scaling.