If you want to accelerate a weight quickly in a single swipe, (simplified) gradually reducing the mass along the length of the whip imparts more kenetic energy at the end (the whip crack).
So the arm would no longer be rigid, although you can see in the OPs video it isn't actually fully rigid.
To make things easier, start with an "integrated sling ballistic" (ie: a piece of thread between two lego pieces). Sling release is actually fairly complicated so chop it out!
The arm is generally a rigid lever, and the sling acts exactly as your "gradually reducing mass". In his design you can see the kindof bike gear shape at the axle and eventually coming like an "A" towards the tip (and reducing to "infinite thin-ness" via the string/sling).
After you've built one simple (small) trebuchet, test to failure! How much weight can you stack on it before a component breaks (bucket? arm? axle? sling? frame?). How heavy of an object can you throw before "everything starts messing up"?
My recommendation for ballistics is mini-marshmallow (desktop), regular marshmallow, mega-marshmallow, then switch to "hard" ballistics, eg: mini candy pumpkin (the connoisseurs choice), tennis ball, basket ball, etc.
Once you start throwing dense, solid objects (marbles, golf balls, baseballs) your risk of property damage and injury goes up fairly exponentially, so stick to marshmallows and tennis balls until you feel more comfortable.
Spend lots of time figuring out safe/reliable trigger mechanisms, WITH A SAFETY! For my tennis-ball treb, I did three eyebolts with a dumb screwdriver on a string, and a vise-grip (clamping) on the far side. Eventually, you're trying to safely "release" 100's of pounds that is being held in tension, and if you have a misfire (fail to release trigger) you're potentially approaching a "loaded" machine which is demonstrably "not working right". Lifting/loading 100's of pounds and then having an unlocked trigger (which _also_ may fail) is not safe for anyone.
You're going to transfer the energy quickly, you'll just break any "arm" that's light enough to accelerate with the energy available.
You could maybe use an 'already broken' arm (rope, like a whip) but then it's not a trebuchet.
Not saying its impossible to create a successful system like that, in fact it sounds sort of a natural/organic design that potential could be closer to the optimal design, but it would be more difficult to accomplish and probably need more testing and design iterations. So I think OPs strategy is more simple and pragmatic in this case.