You know, I think your last proposal of 'training' them is a great idea.
One thing I did as a nanny was to ensure I did the morning and lunchtime dishes and that the kitchen was clean. Not because it was part of the job, but because the kids needed an opportunity to 'go play and find something fun to do'. Even as a nanny I knew it was important for the kids to learn how to entertain themselves, and if I was busy "doing" with them all the time, they wouldn't 'get it'. So, I'd set them up with playdough or something fairly easy for the kids to do on their own and then, when they said "come and see" I would always reply "I'm washing dishes/doing X right now, and I'll come look when I get these rinsed off in a minute." Then, I'd follow through to a natural stopping point. Thus, the kids learned that A. they *could* wait for a few minutes; B. That I *could* be relied upon to go and look at their creations after that few minutes and that C. The adults have important things which need their attention and that it's okay.
I did this with my son, too, and still do from time to time. "Mom, come see."
"Well, I'm right in the middle of the chopping veggies. When I'm done with this, I'll come and see" or "You know, I need ten more minutes to finish what I'm doing, so let's put the timer on. Even if I'm not done, I'll come look in ten minutes. Listen for the ding!"
I do suggest a timer, too. It's a great, neutral way to keep track of time and if you do respond to the 'ding' with your attention for them, they'll learn to relax and go play and just rely on the timer to remind you-- instead of themselves. :) Good luck!