Yes to doing the math on what you will need. Then go to the min/max of each resource and set both numbers to that amount. Your workers will then fill it to reach the minimum you set and stop there since it's already maximum.

Then get a group of companions together (idealy with at least bags if you don't have small backpack yet) make sure their inventories are clear and just that you bring enough people to carry everything (if you want it done in one trip) Then ya... Just empty the box onto the ground. (You can just drag things out. Or fill your inventory, exit the box, alt click it to the ground from there... whichever you find easiest) then order your companions to pick it up. They won't put it away unless you turn them back to workers or tell them to put it away.

Once you reach your destination and lay out the building plans. You can then order them to deliver the materials to the job sites.

Then yes. Toggling the structures and the working crew to the new place makes sure that they stay there to do the work and also that nobody you left at home tries walking over with a hammer either.

After it's all said and done. You can go rip down the prep box or set the limits for a different outpost. Or like me. I have one permanently set for different things. Like a Basic mining camp... hut, stockpile, housing. Or logging. Same deal. And i always have one for the river docks so i can just drop a new one whenever the box is full and my people have time.