I have two old barbags with Klick-fit fittings: but they only fit 26mm handlebars which I no longer have. One is a sturdy Altura pretty much as new, the other is Carradice and much lighter but a bit tired.
You can simply buy ‘oversize’ Klick-fix clips to fit your new 31.8mm bars, if not from the usual mail-order suspects (who are typically a bit useless at anything touring!) then ebay, whence I just got some. They actually came from a chap based in Loxwood, so collection in person would have been an option, if I’d had the time in the midst of moving house!