I would cut the Azaleas back to about a foot to a foot and a half. They should back-bud and grow, but I don't think they'll flower next year if you prune in the fall. I think most Azaleas bloom on last years wood. You could wait to prune them until after they bloom in the spring, that way you wont miss a bloom.

Just get rid of the azaleas.....given the choice :-)) Even being cut back routinely, they will regrow and want to take over again. If you are careful, you should be able to remove the root system once they are cut back but that is not a requirement.

Typically, laceleaf JM's are not underplanted with anything other than groundcovers as their weeping habit typically produces branches to the soil level. If a high graft tree or if trained to be more upward in growth habit, you could try underplanting with something like epimediums, which will never grow too high nor need division.

I would move the azaleas to another place in the garden so you have room to prune the maple. They're in the way now and competing with the maple for water, nutrients, and space.
Mike

Ok - I think the plan then is to move them if possible. I'm assuming fall is a good time, but would it be too early to do it this weekend? Or wait till maple drops leaves?

Wait until the leaves drop and the tree begins to enter dormancy. You are far less likely to disturb the root system to any significant degree if you wait until that time. And disturbing a JM root system is something to be avoided if at all possible.......a good way to introduce some nasty soil pathogens.