Is there such a thing as a water-thin sealant that
I could pour into the window channel, let it work its way through the
leaks, cure, and eventually seal them?



Thanks in advance!!

Yes. Go down to the automotive supply store and get flowable silicone.
It's made to do just that... put it on and it flows into cracks and
crevices then cures up. It's made to seal windshields in cars, but
works great on boats. Just keep pumping it in there until the flow
stops or you run out.