Expanding is going to have to be present if you are to pick up more than 3 cubes. Intakes are probably going to be similar to Toss Up, but also with this magazine of sorts. It would depend on strategy whether or not this would be placed on a lift system, or whether multiple lifts would be needed.
Make sure you design an intake that can pick up cubes from a variety of angles, reorienting them into a known angle, which should allow for you to make uniform stacks. There are a lot of examples if you look at the designs from the 2015 and 2018 FRC Games.
The problem I see with this design is the amount of space the intake would take up. While you would be able to intake and stack fairly well, how would you place cubes in towers. You would need a second arm which would be difficult to fit on top of this mechanism assuming it had to at some point go vertical to stack the cubes. Also, you would only be able to hold 3 cubes at a time with the 18" width restriction unless you were to use a motor to extend the intake.
The intake doesn’t have to be exactly like that. You could store the cubes however you would like to. The point of showing that video was to demonstrate how helpful it is to be able to pick up cubes from any angle, not necessarily store the cubes like that.
It seems like an idea from Relic Recovery could work. You could use the horizontal wheel style intake with an “angler” which would move the cube “holding chamber” 90º in order to stack the cubes. This could be put on a DR4B in order to create high stacks. It would be similar to Team Gluten Free’s design: