Thank you for your question and pictures. You are correct that it could be bacterial canker or a fungal infection. Lindens also suffer from leaf spot, powdery mildew and wood decay. If you notice any holes on the bark, it could be a linden borer. Branches slowly die from the bottom to the top, similar to what you described. Here is an article from Wisconsin Extension about this borer:

https://docs.google.com/viewer?url=https%3A%2F%2Flearningstore.uwex.edu%2FAssets%2Fpdfs%2FA3813.pdf

Since there are many diseases that affect lindens, I would encourage you to consult a certified arborist. It's hard for me to pinpoint exactly what is going on without examining the whole tree. Here is a link to find a certified arborist in your area:

https://extension.umn.edu/planting-and-growing-guides/how-hire-tree-care-professional