"Richard Clark" wrote

A ground connection or counterpoise for the dipole/loop
would be benign in the practical sense. You won't need it (unless you
have lightning phobias);

Well said. And most of us who get anywhere near as much rain as Richard
does (in WA) unfortunately have a LOT more lightning to deal with in the
summer. In that case, shield-grounding the coax of a dipole should happen as
soon as the feedline is down at ground-level, and again at the station
entrance/single point ground, where it should connect to a coax
surge/lightning arrestor.

Perhaps the ground of the BalUn can just go to the coax sleeve?

That will work fine.

73's
Richard Clark, KB7QHC

Indeed, matching transformers such as Industrial Communications Engineers
make, insist the metal xfmr case be grounded for safe and proper operation.
I ground long wires on both an I.C.E. xfmr and a current-type Balun,
directly to ground rods that the equipment is mounted on. This is also the
connection point for ground radials for the long wire, if used.

Best regards,

Jack Painter
Virginia Beach, Virginia