Yeah, the transition can be tough.
Often what I do (may not be optimal) if yes, I leave some behind. Otherwise, I'll take my 1-2 stacks of 1-move units and trudge them to one AI city (usually an inland one). So, ideally, my 2-move units will do a little horse-shoe type of attack on all their coastal cities (bombarded by boats), as my slow stack works its way through to their inland city (cities). So, in a big invasion, my slow stack may only make it to one city, but it's one less my mobile guys need to make it to (or the mobile ones may get there just in time if any of them need a cheap XP to level-up).