If your search for the new owner proves unfruitful, then you have to decide whether you want to proceed without authorization. Even if you are a founder of Google, unauthorized book reproductions will place you in line for a copyright lawsuit. Your two primary concerns are: 1) the likelihood of discovery, and 2) your legal liability. We can't guess at whether your use will be discovered, but the Dear Rich staff can tell you that your liability would include your legal costs, the copyright owner's actual damages, and any additional profits you've earned (unless there is a registration, in which case the damages would be statutory and based on the judge's discretion). In a worst-case scenario, you may have to pay the other side's attorney fees.
You might be able to mitigate your liability by creating an interest-bearing account into which you pay a reasonable royalty -- that is, what a reasonable publisher would be paying the author for such rights. That way, in the event the estate learns of your use, you can offer to pay these sums, which would hopefully demonstrate your good faith and lead to a legitimate license. Keep in mind that under this scenario, your use still constitutes an infringement and the estate is under no obligation to accept your payment.