I got Mustache bars , that Nitto Makes , It used a tube size compatible with Road levers .. But..

the levers lay horizontal so your Brifter function will become unwieldy ..
to swing sideways to up shift, They really need be Upright.

I used older Campag Road Levers , and the gear shifters were in the bar ends.

for the high end fitness bike market there are road derailleur flat bar controls found via Australia and Europe Shimano ..