"That said, I don't know why they'd make the reels with different groove spacing when it would surely be cheaper to make just one right and one left plate, while varying only the core and guide parts."
You have to know and appreciate the history of development of the Lab Box to understand how unreasonable your question is. This was designed by Italians with no prior experience doing this sort of project. Every part of the Lab Box probably had to be fully redesigned at least once while they struggled toward production. For the first 90% of the project, they planned to use one expandable reel for both 35mm and 120, practically a copy of the Paterson style reel. They aren't talking, but it looks like prototype testing showed uneven development using that reel in the 35mm position, as just before they hit production, they redesigned the 35mm reel to add agitators to the exterior, and the prior reel, now the 120 reel, lost its multisize adjustment capacity. (The agitators make the 35mm reel too wide to expand for 120 and still fit in the tank.) Lab Box is a classic example of a grand design idea finding the devil in the details, which is how they spent the 700k euros from Kickstarter doing a project orginally budjeted for 120k euros. At least, they got a good product to the backers, which must be a high watermark for any KS project.