Yes, that is a great feeling! I wasn't sure what Princess' policy was on that, but figured it couldn't hurt to ask. The rep I spoke to re-fared it without a problem. Like you mentioned, that's more money to spend onboard / on excursions.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)