The first time we had our son (4 YO) on a pullman, he tried to climb down first thing in the morning for the bathroom and accidentally fell... a medical center visit and several stitches on his forehead prove that your concern is not irrational at all.
When we sailed with kiddos, it was not pulled down either time. One time we asked them to, and the other time, the kids shared the couch... entirely up to you.
I was not aware that they resumed port day drop off, or if it is available for all ships in the fleet. However, if you are looking to "leave your child for a few hours", as asked by the OP you will be required to pay hourly for children under 2.
I think you got lucky. I submitted mine 11 days later than you, and still nothing aside from the 'acknowledgement' e-mail. Ones in the past have taken me a few weeks.
This is the information from the Shareholder information document.
Guest Administration
3655 N.W. 87th Avenue
Miami, FL 33178
Tel 800 438 6744 ext. 70450
Fax 305 406 6102
Email: shareholders@carnival.com
I think 2 hours is really generous, even with traffic... normally that would take closer to an hour. That being said, some of that will depend on customs. My last trip on the Panorama didn't start ANY debarkation until after 8:30 because customs was short handed or something like that.