Assuming the water pump is not failing internally, you said the mounting screws are tight. They should be somewhat loose to allow the rubber mounts to absorb the vibraiton. Also check that no PEC tubing is touching any of the cabinet/floor. Any vibration will be transferred throughout the structure and heard as a loud rumble.
You said the pump sounded loud "internally" I don't think there is any "air pocket" or purge procedure that will help with that. You may have had a little water left in the pump that froze and deformed one of the valves. If so, you can buy a new head for most pumps, but with flojet, it may be cheaper to just replace the whole thing...
If you're still under warranty, get it to the dealer quick as you're about at the end off warranty on a one year old RV. However, if your water pump is a flojet, check your warranty, most of them are 2 years