helms

Hi all, I have this cold running problem with 2002 IS300 (210k km) that I think is blown head gasket but I'm not convinced 100% yet. Maybe somebody can help guide me further how to diagnose.

Symptoms are following:
The idle is really rough like half cylinders are not working at all when engine is cold in the morning. It starts fine, revs over 1000 and after about 15 seconds drops to ~600, shaking heavily. When I put gearbox to drive the rpm drops further and engine stalls. After stall I need to crank 5+ seconds before engine slowly begins to start. Also I see white exhaust smoke.
When trying to drive right away, acceleration is bad. With full throttle it only slowly accelerates and not downshifting gears normally.
All those problems are almost gone when engine is hot, only very subtle trembling remains. Acceleration is perfect, engine revs 6000 and shifts fine. No noticeable exhaust.

Some facts about engine condition and what i have changed myself and checked:
*Engine has at least once overheated to such level that steam comes out. That was because of failed radiator cap and low coolant level. I suspect previous owner has had the same event.
*Coolant level is lowering, about 1/4 gallons in 1000 miles (maybe it leaks constantly with time and not related to mileage, don't know for sure)
* after about 100 miles, sometimes throws P0430 (catalyst system efficiency below threshold (bank 2)), happens on highway at constant speed.
*Engine does not noticeably eat oil.
*Oil is not milky, looks clean.
*Coolant is not bubbling when engine is running.
*Have done compression test, all cylinders are consistently between 12,5 and 13,5 bar.
*Changed spark plugs, old ones are only a little bit different colored. Light gray center isolator.
*Tried spare ignition coils (3 pcs).
*Measured high voltage cable resistances, all normal.
*Cleaned throttle body, MAF - no change.
*No visible leaks in vacuum tubing, PCV valve looks fine, also cleaned.
*Air filter is changed, pipe has no cracks.
*Used "injector cleaning" fuel additives once, did not have effect.

What makes me doubt about gasket failure is consistent compression and clean oil. Coolant leak could also be anywhere in system. Could be that compression levels are not legit as engine was not totally cold when I measured but problems are excessive only on cold motor.
I can think of two other options - too rich mix or failing ignition driver (some transistor or whatever thing that drives ignition coil maybe not working fully when cold).
What should I test further to narrow exact problem down?
I'm thinking about leak down test (cannot do myself so it takes time to get results).