If the taxpayer has already signed a contract to sell the relinquished property, is it too late to start a tax-deferred exchange?

No, as long as the taxpayer has not transferred title, or the benefits and burdens of the relinquished property, she can still set up a tax-deferred Exchange. Once the closing occurs, it is too late to take advantage of a Section 1031 tax-deferred exchange (even if the taxpayer has not cashed the proceeds check).