Any of those will do what you want, but they are very different bikes. The specialized and kona have drop bars, the trek has basically flat bars, and I'm not sure which Giant you were linking to - I just got the home page. So, it kind of depends on what riding position you're comfortable with, but they're all good bikes. As far as sizing, if you think you need a bigger size, I would definitely try to find one to try out. And no, you aren't being overly picky.

The Jakes run big for their stated size (at least they have in the past, unless they have changed), so you might want to take that into account.

Also, do you plan to use a rack and panniers? At 6'3", you probably have pretty decent sized feet, and will want to prevent heel strike. The FX has the longest chainstays at 445 mm. The Tricross is almost as long, at 440 mm. The Kona is shorter at 425 mm. Again, not sure which Giant you are interested in. Any of these can probably be made to work with the right rack, and with panniers that have a robust mounting system, but it's something you should probably take into account if you want to use panniers. Just my two cents.

As far as your stem question, I don't think it would affect the handling noticeably, but I really have no experience with things like that.