i can offer a possible starting place for your project. (first, a short disclaimer: i do not advocate, recommend, suggest, imply or in any other way endorse reading any further; should you choose to ignore this notice, i will not be responsible for any damage, injury, hurt, disappointment or regret--inconsequential or inconseigural--resulting from your actions).
use an empty 5 gallon plastic water bottle as a bat to hit a citrus fruit (orange or grapefruit) ball. pretty cool huh? (its also cheaper than using a beer bottle to drive golfballs).
this concept might just lead to the 'soul of a brand new seige machine' that looks outside the box & into the empty container to provide hitherto untapped sources of propulsion.
Presonally I am partial to the onager for ease of aim. Getting the release point on the trebuchet is quite tricky.
It was also my experience in tabletop an history that led me to this conclusion. in that time frame "more" was always better..... (for siege engines)