But, as a more or less theoretical question, to minimize the
possibility of
lightning hitting the antenna at all, or inducing large voltages in it,
is
it better to just leave the now "floating" antenna alone, or is it
better to
ground one end of it ?

Why ?......................................

I prefer to ground all the feedlines. I have a ground strip outside
my window with a bunch of SO-239's. I just screw em all in when
bad wx is around. I doubt it will make much difference as to the
likelyhood of being struck. Horizontal wire antennas are not struck
that often compared to verticals, trees, etc.
But if it is, I'd prefer it to be grounded to reduce flashing, etc.
My metal mast takes the brunt of the strikes to ground. All
my grounding of the feedline does is take any left over energy
on the coax to ground. Same for induced energy from near
strikes. And it can be a good bit, as I actually can hear my
connectors arc with nearby strikes. Never leave antenna wires,
or feedline ends in the house, or in bottles, etc..You want it
out of the house if it's not protected. Even if using a grounded
switch, etc, I'd prefer not to have it running through the house.
IE: ground wire leading along the wall, etc to the switch to
ground it. Most switches ground the unused connectors, or
have a ground position. I don't like those in the house if the
feed is unprotected by gas tubes, etc...
MK