Home Exchanges don't have to be simultaneous. 

Recently we received an email from a couple in The Netherlands who wanted to do a home exchange.  Unfortunately, we had to tell them that we were in no position at the moment to consider a simultaneous exchange.  However, we suggested that they might wish to stay in our home while we are away on a trip to the Eastern provinces of Canada during the period they wished to visit.  This was with the understanding that at some future time we would avail ourselves of the opportunity to stay in their home in The Netherlands.  This would have to be at their convenience and at a time when they would expect to be away from their home.  They accepted the idea, giving us the assurance that this would work for them.   So next year they will be visiting Canada and staying in our home for a 3 week period, giving us the pleasure of looking forward to a time in the future, as yet undetermined,  when we will visit The Netherlands and stay in their home.

The point is: home exchanges do not have to be simultaneous.  We worked it out in our way and there may be other ways this could work, especially if you have a second cottage or a second home where you could stay.  The point is there are many different ways in which a home exchange can work to the benefit of both parties.