I detest(ok, HATE) calcium filled tires. It's ruined(ok DESTROYED) 6 of 8 original PA rims for my D-14s( $$$$$ !!). Replacing 55 year old rims is very,very costly,repairing can take 1-2 weeks if done right. Maybe, maybe if you're the first one to add it, done 100% proper and maintained and NONE of the saltwater ever comes out, the rims may surive. Get a thorn or nail into a filled rear and ,well, that's 'game over'.....
I've kept the BH on my BX23S as 'ballast' as I use the loader a lot with both bucket and pallet forks, haven't need any extra weight out back. I can see using a ballast box as your best choice as it'll come off for 'grass mtce mode'. The BBox can be compact(close to tractor) for easy manuovering.