^As far as I understand (I've never used Luxire...yet) you can take your best fitting shirt and send it to them to copy. You'll have a perfect fitting shirt customized anyway you want (material, cuffs, collar, pleats, etc.). Prices are either in line or actually cheaper than BB.
I'm going to send a pair of pants to be copied soon.
Another option is Kamakura but you have to sort out what fit you are.