Baby monitor was my first thought as well. A kitchen timer would work too, as you most likely use the same cycles, and the time should be about the same each time. For me, after the first load, I just have to wait for the dryer, which has a buzzer. I really have no need to be there precisely when a load is done...
A wireless doorbell probably wouldn't be too tough to wire in there either. Some cordless phones have an intercom function between the base and handset, not sure if it requires an actual phone line though. Something to look into, as I think land lines are really dying out these days, phone equipment is getting dirt cheap.
I would definately look more to a non-invasive solution, control boards aren't cheap. My neighbor's GE got knocked out by lightning, new board was $157 plus shipping. I found a similar transformer in my junk, and got it working for free. I just gave the washing maching back to him, because I knew it was likely to fail again, not much protection for a digital circuit. My washer is more the 20 years old, all mechanical, sits on an open back porch.