What are some meaningful forms of white space training that as a platoon leader I can make sure my unit experiences?

Look at the METL Cross walk and see what are the reoccurring supporting individual tasks , those are your high pay off tasks. Start there. sRehearsing unit SOPs, especially Platoon SOPs is time well spent. Do all those things in MOPP IV. You also have to look at your uNit mission, what is important to a Support Unit may be different to Infantry units. Quartering parties and occupying a patrol base is always time well spent. Range cards and sector sketches.

Look at the unit training schedule and see what tasks are coming up that your Platoon is unfamiliar with. I would also say that white space is a great time to catch up cyclic inventories and hitting the MP to get the parts received not installed report. Hang parts and inspect vehicles. Fix load plans. Make sure you don't have random shit in your containers.

Cross train everyone on Platoon equipment including radios, TACSATs, and battle command systems.

Depends on your unit and mission. I'd pick 5 essential training tasks that my unit must complete. Of those 5 tasks you will have some tasks that overlap. Tackle those and be an expert in those areas. It could be filling a radio in the blind, reducing a trench line, BDAR on a weapon. Rehearse those tasks and make them your units main battle drill. White space is a premium so when the Gods allow it have your plan written, follow the 8 Step Planning Process and Troop Leading Procedures, execute, and conduct an AAR after every task.

Naps. Now before you laugh, consider this: Physiologically speaking, siestas (as practiced in Latin nations) have been shown to match the human body's rhythms. Sadly, I didn't discover the value of napping until I retired. I always knew I did my best work in the morning and that my work time after lunch was never as productive. Now, I find that a nap recharges the batteries better than anything else. I find it humorous that someone discovered this simple fact and gave it a fancy name - "white space" - and is probably making a fortune off of it. But white space without sleep is a poor substitute for napping.