So, we have some managed switches where I work that have SFP (or mini-GBIC) ports. From what I've read, those max out at gigabit speeds. I guess there's a SFP+ that does 10G, but these aren't that ...

I never use them if I have a choice. Your Fortigate doesn't have an SFP cage but going to a 90 model does, I think. That is what I would do if you want to use fiber long term. Media converters are ...