I have a lot of experience with this since my husband and i travel all the time for work. We have three cats. I agree the 6 days is a lot of time for them to be alone, at least having someone come in and feed them and clean their box is a good idea. Just having them come in is a good thing wether the cats like other people or not.
I have left for over 6 weeks at a time. When I get back they act like they don't know who I am. But after a day they won't leave me alone. My one cat Bo won't leave my side (it's so cute) and he does that meowing thig too. I have had a friend who said that thier cat lost he's voice from the meowing after they got back from a trip too.
I red once that they think you have been dragged off by a preditor evey time you leave. I don't think i believe that.
I would get someone to look in on them. You know just in case they need med attention or something. My cats get used to their sitter after about the 4th day. good luck.