in the dim and distant past when I worked on BMW's for a living, the M20 was the common engine in 3 & 5 series. We would commonly replace rings and valve stem oilseals due smokey engines. The carb'd versions would start to run rough when they started to breath due to rings. You could cheat a bit with those by disconnnecting the rocker cover breather and running a length of hose down the engine bay to breathe to atmosphere. The injected ones didn't like that trick though.
Valve stem oil seals would go hard as suggested by
@Grumpy.
Smoke on start up could suggest valve stem oilseals, small amounts of oil passing the seal and collecting either in the combustion chamber if the valve is open, or sitting on top of the valve if closed.
Smoke on hard acceleration though, points more towards rings.
If you remove the oil filler cap while its running, does it "breathe" fumes?
Are there traces if oil in the inlet tract where the engine breather is connected?
Both would suggest a bit of ring blow by.
static compression test will highlight this.
How much oil is it actually using?
If its any consolation, the aeroplane burns and breathes half a litre of oil per hour. If we are flying out to another airfield, we take a bottle of oil with us!
