Any possibility the leak around the vent is coming through the vent itself .... ie. it is not closing securely? Do you have MaxxAir (or similar) vent coverings installed over the vent (so it can be left open when raining or on the road)? As for the floor, work from the top side. If some wood needs to be replaced, it will have to be done from the top anyway. I'd start with the section near the door. There is probably some molding at the entrance that can be easily removed so you can lift the linoleum and see what's happening.
Kevin, Barb and Jake (the Golden/Lab Mix)
East Bolton, Quebec, Canada
2012 Infinity 3640RL
2012 GMC 2500HD Diesel