Just noticed this thread was updated, and with videos!
Looking back (page 7, post 99), July 1st was your first test fire before construction was complete. At that time you had no idea how to run an offset or if your design would work. Now less than 8 months later it looks like you are the master of a fine machine! Congrats!
My suggestion on mobility would be to add weight to the nose and ditch the casters under the firebox. The big question is what to use for weight. I would suggest a ceramic kamado, but you seem to have enough charcoal burners already, so how about mounting a propane griddle like a blackstone opposite the fire box? The weight of a griddle and a propane tank should be plenty to keep it from being tippy, and there is the added benefit of having another very useful cooking toy.
One other thought watching your workflow...you need a shelf. Use a little expanded metal and make yourself a shelf under the door opening where you can set down your trays of food. You can make it fixed or fold down if space is a concern. Just make sure you mount low enough so the door can open or close with a butt or brisket sitting there. I have one on each side of the Lang and they get a lot of use holding food, tools, rubs, mops, oil, trays, sampling knife, etc. during any cook.