To my mind that stand is too narrow. Barely a foot wide. Needs bolting down.
Oversimplifying the magic number for cupboard or tilt stability is 2 ft or maybe 18" if its not got serious weight on top. Anything significantly under really isn't stable unless restrained. Personally I'd DIY something of similar width to the table.
Perhaps bolt a couple of two drawer filing cabinets together with a strong shelf above (kitchen worktop?) to hold the mill and a stash drawer for lightweight stuff between cabinet tops and splash-tray. Filing cabinet drawers hold lots of weight so good for tools et al. make half depth lift out trays, two or three to a drawer, for lighter stuff.
Clive
PS So I'm pussy. Seeing Bridgeport dropped sideways off a pallet truck leaves blasting impression!