Which I wouldn't mind if it was seconds, but in several cases recently, said conversations opened this end over 3 hours after my contacts started them, by which time of course, they're offline, so I can't continue them.

I have no idea how I'll reproduce this for you, if the contacts involved didn't refuse to use another IM solution, I'd move to whatever other they had and simply ditch the new broken Yahoo. Consequently I have no real-time method to get them to start a conversation ....