2006 Convertible - Top Difficult to Close

I have a 2006 convertible and the top stops about 2 inches away from the windshield when I try to close it. Sometimes I really need to wrestle with it to latch it closed. The dealer says Ford's technical bulleting tells them to place the vehicle in a body shop paint oven for 2 hours to try and stretch the cover and if that is unsuccessful to relplace the top. I live in the Northeast and it stays in the garage for 5 or 6 months a year (with the top closed). The car only has 27K miles and it's in mint condition including the top except for the shrinkage.

It ticks me off that the cover needs replacement so quickly and my Ford Premium Care won't cover it. I am wondering if anyone has run into a similar symptoms with more reasonable solutions.