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About the axle length. I had trouble finding this with my RRA as well. Endied up getting a Bayliss wiley raleigh specific one if the end. (Cottered.) Seems to work pretty well with a sturmey archer hub but not sure whether that would translate well with fixed. The Chain line is good, although not quite perfect if I remember right. I'll have a little look see if I can find out for sure but I think it was one of these:
Pretty sure thats the chap I bought it from (he seems to have a never ending stock of NOS Bayliss Wiley axles for some reason.)
The RRA had its own specifc bottom bracket axle-you could try searching around or V-CC or something to see if anyone knows the length of this I suppose as well.
the brakes did not have all the mounting hardware I needed. Given the bike is not being a ridden at present as I can't stop it in an emergency it is all academic. the curved washers I have dont fit properly so I will have to find a solution, may have to make something
Yes I still use the Dawes, it i the family town bike for popping into town and the like.
the bars are renoylds but I am actually bidding on these at the moment http://www.ebay.co.uk/itm/272465345917?_trksid=p2055359.m1431.l2649&ssPageName=STRK%3AMEBIDX%3AIT
the bars pic you posted would be perfect. Been looking at a few different Nitto bars as well. Can't make up my mind what I would like. I probably have to buy a collection of bars and then try them all out. It will keep me amused at least.
the stem and the seatpost are far enough into the tubes to not cause a problem. However a longer seatpost would be desirable but not actually essential. Just finding the parts I have so far has been a patience game. I'm in no rush eventually it will come together.