It's much commoner in Scottish music to go from duple to triple time than the other way round.

Sleep Soon i da Mornin is 2/2, not 4/4. Normally you keep the beats the same length in this sort of transition, so 1/2 in the reel takes the same time as 3/8 in the jig. But if you have some specific musical idea in mind and no external constraints, almost any tempo relationship can work.

The one time when you must get the timing equivalences right is when playing marches for a Gay Gordons. It's common to mix 2/4 and 6/8 marches for that, so 1/4 in 2/4 = 3/8 in 6/8. Any deviation and the dance will go haywire.

Incidentally Drummond Castle is basically the same tune as Cutting Bracken but in a different metre - it's quite effective to go from Cutting Bracken into Drummond Castle.