- it is , for me
anyway, virtually impossible to actually measure the diameter of the
hole via the telescopic bore gauge/micrometer method,

I understand convictions like that. I was certain for 40 years that I
could never hit the other side of a room with an M1911. I now have 2
of 'em and I can hit the other side of a room with both. G

Telescoping gages are fiddley, but they are somewhere between useful
and indispensable in a task like yours. A machinist must be able to
measure accurately. Get someone who is capable with them to coach
you a bit. Plan on spending a patient hour or whatever it takes to
become functional and comfortable with these tools. It'll be a
good investment of your time to gain a skill you need and will use.

Boring heads don't always or often get things "tits" on the first
pass. Make subsequent passes until the tool is no longer cutting.
Things flex and wiggle under load, the only question is how much. This
is particularly true in home shops and in schools with old machines
that have seen a lot of use.

It is possible to do the task you describe with a boring head on a
mill, but for accurate work I would choose a lathe whenever possible
because it is possible to get a more rigid setup and it's easier to
sneak up on a precise dimension -- once you can measure your work.
Grab your work on a faceplate or in a 4J, center it (more fiddly
work), then start boring. Again, as you get close (within a thou or
three), make more than one pass without changing anything on the
machine. This doesn't always work well with stainless but that's
another matter -- it works fine with mild steel, ally or brass and a
sharp, well-ground HSS cutter. Use carbide tooling on cast iron.

Flap paper is not a good approach because it can give you an hourglass
or barrel-shaped hole. If you want a precise cylindrical hole you
must generate it with rigid tooling. Fine finishing can be done with
a lap or rigid hone, but that isn't necessary for a bearing housing
and particularly not for one made of ally.