Are these genuine Moller 71 chairs?  

They look right to me.
It is very hard to tell if the 71s are earlier or later. (The 55s are much easier to tell apart). The earlier ones may, or may not have a Møller medallion; Møller was quite inconsistent with putting on medallions. The later ones will have a Møller stamp, although it can be very faint and covered by upholstery/cord.

Thanks Leif, what would I do without your amazing knowledge!

Here are some more pictures, some of them are a little rickety. Someone seems to have put rails on the legs of two of them(Ugh). The upholsterer also put triangular supports in the corners. I can't find any makers marks on them but I haven't taken the upholstery off them, I just peeked under one. What on earth will I do about the two with the rails added?

If I remembre well, the stamp / medallion should be right in the middle of the rail. On one side you should have the Mollers mark and on the other the Danish Furniture Control one.
I have owned a few #71 chairs and not all of them were marked. Yours look legit to me.
My guess is that the rails on your chair have been added to consolidate a broken chair. If you look at picture #3, you can clearly see that one of the legs of your chair is cracked which doesn't smell too good to me.

Many years ago I went to view a set of 71's a lady had for sale. A couple of the chairs within the set looked off to me.
I turned them over and stamped underneath was a makers name and 'made under license in Holland'.
I took pictures of the makers mark for posterity (but have since managed to lose them). The chairs were ever so slightly larger and less elegant than a legit Moller.
I've never seen another one since but one can assume the copies are out there.

I've borrowed a friends 71 to compare and they're identical, so I'm not really worried about them being genuine, I'm hoping I'll find makers marks at the reupholstery stage!

Early (as in pre-1971-ish) Møller product is actually quite infrequently marked. There are many tables that are Møllers that are routinely mis-credited to Johannes Andersen, because they bear a striking resemblance to his work, and are mis-credited because they are not marked.
I have 19 Møller 71s and 55s laying about the house. The latter ones are all marked, only half of the earlier ones are.
Anecdotally I believe the the production from the 50s was less frequently marked (this is when Møller made more tables). The chairs I know are from the 60s are more frequently marked.

Early (as in pre-1971-ish) Møller product is actually quite infrequently marked. There are many tables that are Møllers that are routinely mis-credited to Johannes Andersen, because they bear a striking resemblance to his work, and are mis-credited because they are not marked.
I have 19 Møller 71s and 55s laying about the house. The latter ones are all marked, only half of the earlier ones are.
Anecdotally I believe the the production from the 50s was less frequently marked (this is when Møller made more tables). The chairs I know are from the 60s are more frequently marked.

Leif I would fricking love to see 19 Møllers just hanging out!! I'm going to get them reupholstered eventually so I'll see then if there's any marks on them. According to the seller mine have been in use since the 50's.