Just one thing: saying Achilles and Patroclus were "best friends" is a huge understatement and makes no sense at all. I think "Lovers" is more accurate and better reflects the following rage of Achilles. Which is also foreshadowed when Achilles captured lady is taken away, he makes a big deal of that.
Greek wars had no place for Heterocentric views.
I re-read it a few years ago, and couldn't find any references to it. It may have been because of the translation of course, but I don't think so. They are cousins and best friends here, and there may or may not be more between them, but it's not mentioned.
The book (a play) in which they are definitely lovers was written by Euripides.
By the way, when Briseis is taken away, and Achilleus is enraged, it's not because he loves her so much. It's because she is his slave, his property given to him by military right. He'd be just as enraged if he had a beautiful horse taken from him. Yes, that's hysterics. :) The heroes of the Iliad are pretty childish in general.