I think you're confusing the "cloud" of smoke with
"noxious smoke".   Think about diesel engines - many
output smoke as a daily routine.

Thinking back to my courses in organic chemistry:
Any good antifriction material will act the same way - molecules
slipping over each other.  The larger the molecule the better the
antifriction ability.  It takes energy and oxygen to break down and then
oxidize the smaller parts.  Injecting oxygen into the system at several
hot points should oxidize the broken HC molecules...
Hmmm... sounds like a catcon witn an AIR system.

It was a Chrysler/Dodge/Plymouth with a 3.0-litre Bitsushitti V6 engine
and less than 70k miles on it.

The O2S and the rest of the closed-loop engine management system has no
effect on the amount of smoke produced by an oil-burning engine. The
catcon consumes a great deal of the smoke, but a great deal more still
remains.

No.

Better and less expensive: Fix the older vehicles so that they don't burn
oil.

Well mostly when they ingest enough oil via worn-out rings, yes. Briggs &
Stratton lawnmower engines can run on a dry fuel tank, too, when the
engine's worn enough and the oil's contaminated enough.

One problem with this is that most of the oil emission is NOT from
burning oil, it is oil vapor.  We use the term "burning" somewhat
colloquially.  Pour cooking oil on a hot frying pan.  See the somewhat
bluish white vapor?  Most of it is not combusted (burned) oil.

What happens to most of the oil in an SI engine is that the oil reaches
the boiling point after touching hot metal, boils off, comes out the
exhaust or breather, and cools enough to start condensing in very small
droplets.

Situation in a diesel is different.  Here, the fuel (oil) is indeed
partially (actually- mostly) burned, but some carbon particles remain.
Believe me the industry has spent many man years- probably man
centuries- trying to reduce or eliminate smoke (carbon particulate
emission).  If you can come up with a way, you can achieve fame and
fortune, but it is not an easy task.

Back to spark ignition- if you can come up with a lubricant that will
lubricate as well as oil, but has a boiling point higher than any metal
temperature it is likely to achieve, this would be a great thing.
However, years of trying so far haven't worked.  This is one of the main
roadblocks keeping people from productizing adiabatic engines.

I don't think visible smoke is the real problem.  Even if we would
design a lubricant that would burn invisibly, it would still be burning
and polluting.  The real question I think is whether the owners of
vehicles with worn out engines should be required to repair the the
engine or take it off the road.

Engine by Mitsubishi, no doubt. ;-)

Synthetic oils (at least Mobil 1)  hardly smoke at all when used in an
oil burner. HOWEVER- who would pay the $$ to feed synthetic oils to an
egregious oil-burning engine? Thats how I even found out that synths
don't smoke. I switched my tired old 300,000 mile '66 383 back over to
conventional oil when oil consumption got out of hand, and it became an
instant smoker. Put it back on Mobil 1 (just to see...) and the smoke
quit. Same grade oil, same RATE of consumption- just no smoke with
synthetic. I retired the engine not long after that and built up a 440
to go in its place.

Aside from that, I'll bet that even though they don't smoke, synthetics
still pollute quite a bit when burned in a gasoline engine. A fluid with
the long-chain polymers needed to lubricate well just isn't going to
burn very completely in an engine optimized for gasoline (I'm not a
chemist either, just an educated guess).