The peak power of your motor is 20KW. This is all that actually matters.
You need a battery capable of delivering at least 20KW. That would be something like 270Amps from the battery at 72V.
So, in my opinion, you will need your battery to be able to deliver at the very least 300Amps peak, since the battery must always be the most powerful component of any build.
Your boss suggestion is unfortunately probably not the best. I wouldn't do that. Lipos are dangerous if not very closely managed, plus 12Ah of capacity is very low so you won't have much range unless you parallel 2 or 3 of them, but then it's even harder to monitor. Also they have a very short lifespan, expect to replace the pack every year or two years. Sure they are the best if we're only talking about raw power, but they have just too much drawbacks.
I think that some pictures of your frame might be in order, all will depend on what space you have available.
But anyway, big picture is that you need a battery capable of at least 300A peak. Continuous ratings don't matter on our vehicles, as we can never run at full throttle for a very long time (there's always red lights, turns and whatnot). LifePO4 is my favorite battery chemistry because it has decent discharge, very long lifetime and it is relatively safe to work with. The only drawbacks are size and weight, but if you can afford it then go for it.
The peak phase amps are not relevant to the battery sizing, you can have very high phase amps yet very low power drawn from the batttery, those are independant things.
