FP- yeah, not good for uploading alongside FTP. It caused me problems with "invisible files and folders" on the server - the advice from my tech and M$ is that you shouldn't be doing both in tandem.
Anyway, I guess the best answer depends on what is in each folder and how many folders you have.
If there are not many folders outside the ones you dont want to publish...use CTRL + click on the folders you want and right click to publish.
If there are a ton of other folders and that would take too long, you can select the log files in each folder and set them to "don't publish"
As for directly tagging folders not to be published....I ain't seen that option :(
Otherwise, IE aint bad at copying....just go to FILE > (check the open as web folder box) and type in your address
drag and drop what you want to put on the server.
They are workarounds if you can't find what you want :)