JimE wrote:

...The problem is that there is only a 240v 3 wire outlet on that wall.
This outlet is what powered the old unit, which also had 120v outlets
on it that were powered by this outlet.

Note the words "on it." I suppose it would be legal to plug a fridge
into one of those outlets, if you didn't remove the old unit. If you
removed the front door of the old oven, would it still be legal to
plug the fridge into one of the 120 V outlets? Probably so. And if you
removed the range top? Probably so. And if you removed the racks in
the oven? Probably so. And if you removed everything else you could
unbolt or cut off, leaving only the outlets, dangling by wires...? :-)

I need a 120v outlet to power the new fridge and it appears that
the only reasonable option is to tap off one of the hot legs...

Essentially duplicating what was on the old unit, with no change in
the existing level of safety. I wonder if there's some way to improve
the level of safety with something like a gfi, with no new wiring...

Nick