Windshield sealing issue

[scotty64]

My new to me '64 windshield is leaking at the rubber molding/glass junction. The windshield and molding are recently new (done by the previous owner). The installer would be happy to fix it for free, except that he is 370 miles away. The first glass shop I contacted here said "Those things leaked from the factory" and was unwilling to touch it. Before I get blown off by every glass shop in town, I thought I'd check with the group for possible thoughts and suggestions.

Thanks.

Scott