The 'smokers' were nearly always -22B engines, the -524 series hardly ever 'smoked' in my sixteen thousand hours on type.
I also would debate your claim that a wing engine, if started in isolation using only APU bleed air, will spool up quicker than No 2.
Debate aside, that has been my experience.
Normally, old time Flight Engineers have wanted to place a small wager on the point...I prevailed every time, using the clock.
Imagine that, they actually learned something from the Commander...