Mike: We had the same issue with our 276SR.
I replaced the seals around the doors, and then did the nighttime "light in the compartment" test. Found that the doors were actually slightly bent and some judicious straightening (bending) of the door panel fixed the leak.
As to the carpet, we used a carpet machine with a hand held attachment to clean/dry the carpet. Our entire front carpet, in the hatch, under the bed and all around the bed was wet. (It's all one piece of carpet) The machine got the carpet dried to slightly damp, then we used a small electric heater and a box fan to completely dry it out. Thankfully, we have a maxxair cover on our bedroom vent so we could leave the roof vent open while we dried out the inside, the compartment was a little trickier, but the small heater fan dried that out too, just had to babysit the open compartment.
Good Luck,
Mack
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2004 Dodge Ram 2500 Club Cab 4x4 CTD
2007 Sunline Solaris T-276-SR: Misty Blue/Cherry
2001 Dodge Ram 1500 Reg Cab 4x4 OFF-ROAD