I think for friends I would go for the very direct no.6 (Could you take your shoes off, please?) and for people I did not know, I would use the more restrained no.4 (Are you alright with taking your shoes off?).
It may be that you are just too shy to use the more direct requests. However, you might find that the softest approach no.1 works a lot of the time. If you are barefoot and there are a lot of shoes by the door, you may get the right reaction just by saying:
You can take your shoes off here, if you like.