"I must say, to go from 6/8 to 4/4 without a pause, even a slight one, seems a bit unnatural."

That may be so, but it's the norm for Cumberland Square Eight, which usually alternates 'My Love is But a Lassie Yet' (4/4) with 'Atholl Highlanders' (6/8)... 64 bars of the first, 64 of the second, 64 of the first again and so on.

In that example, the crotchet is matched to the dotted crotchet.