I watched a full inventory speedrun and realized that if this is allowed it would save tons of time

Is it possible that you could get lots of one item and fill your inventory with it, for example if you get 1 stack of oak planks and then click and hold RMB, you could move your cursor over each inventory space, filling them with an oak plank.

I could see why this wouldn't be permitted, as most of it would be menuing.

No it needs to be a unique item in each slot

Its not allowed, it has to be individual items or full stacks

Read the rules, it says every item must be unique. It's like that to make it actually fun.