Tanker (aka Appropriately Paranoid)
We have a 2005 22' CCD and like you found leaks at both the front and rear ends. In our case the evidence of leaking was found before the floor rotted away. We first found mold and damp OSB flooring in the front while converting our front bed to a couch.
Photo when found and
after fixing leaks and painting the floor. Since the front end floor is completely covered by the couch and cabinets we did not reinstall vinyl against the outside walls. We left painted, exposed OSB flooring around the outside edges and can now easily inspect for leaks.
The rear floor is visible, however, beneath the desk. We therefore fixed the leaks, painted with a marine epoxy paint around the edges, and reinstalled the vinyl. We frequently run our fingers around the chrome trim that you describe to check for moisture. We also remove the desk drawers and visually check exposed flooring beneath the furnace.
An area that has stumped us is how to check for leaks beneath the shower pan (rear streetside on our trailer). We have installed a small computer-style fan in the plumbing access panel door in an effort to circulate air beneath the shower pan.
Even though our floor plan may differ from yours, possibly our experience can help you.