I rescued a 1 year old dog with this problem. So far, the behavior hasn't completely gone away but it has been greatly improved.

You are correct in not punishing him and cleaning it up without him seeing it.

Here is what has been working for us. We ignore all the animals upon leaving and returning home. No words are spoken and no eye contact is made. We go straight to the back door and escort the overly excited dog outside by herself. Still no words are spoken, we point to the area where she goes and we wait. We ignore her attempts to get our attention. When she has done her business, she gets praise and attention.

We always leash and unleash outside or in the garage. We remind our guests outside our front door to ignore the dog until she has calmed herself down. All communication with her are in a calm monotone voice with absolutely no excited baby talk.

We take her out about every 4-5 hours and watch her to insure she empties her bladder.

There has been great improvement.