I have a similar problem but just a mere 500 extra long links. I have whittled 1,148 broken links down to 22 and aiming for zero.
With the titles too long do I need to worry where I have linked out to other sites in a post that that might create new broken links or are there other things I should consider?
I always understood that I could fill that title bar and there would not be a problem. On examining the offending links I see that as the domain name has 32 characters from the first www to the m in .com which when prefaced with http:// and the title in the tilte bar creats a huge url. (I know the domain length is pushing it and know about the number of characters for Adwords)
So I just change the title in Yoast and don't bother about the title at the top of the page and the prermalink that was originally created?
I will do whatever it takes to clear up the problems but would like to sort the title links in one hit as I go through page by page.
Your advice would be appreciated.