Don't beat yourself up too badly John---we've all missed the so-called "obvious" in our pasts.
Not too familiar with what access you have to the underside of that opening but I'll throw something out.
If the opening hasn't already been treated with POR-15 or its like I'd do that first. Next I'd get a piece of 1/16" or 3/32" rubber sheeting and make a "reverse boot" for the underside. It could be attached to the under floor with something like 3M's Super Weatherstrip Adhesive which is pretty much weather-proof.
You'd form the rubber sheeting similar to the top boot so the shift lever can move through its normal motions without stretching it.
I do wonder though how wet or soaked is the carpet & padding now?