unless it's a simple gotcha like the oil filter not screwed on properly
or the breather hose absent, i'm not sure it's economic to spend much
time diagnosing what's wrong with this motor - based on symptoms, it
could be something serious like a thrown rod.  look into the economics
of simply replacing the motor.  a jdm import is $300 - $400 for the
lump, plus labor of fitting.  a good deal cheaper than the economics of
any but the most basic repairs.

do you know any manufacturer that doesn't cast piston rings?

there are cases where honda rings crack and leak.  but many honda motors
routinely last 300k+ miles with no problems.  my old crx was at 306k,
ran like a champ and didn't burn a drop of oil.  how does that compare
with gm or frod?

a leakdown test is usually to see the finer details of engine health.
if this motor's burning 4 liters [that's nearly 8 pints] of oil a week,
doing a leakdown test is like using a rule to measure the spacing of the
deckchairs on the titanic.