My bar choke broke years ago.
Mine's Ivanised so doesn't often need choke.
But when it does I just grab the choke slider on the carbs. It doesn't move far but more than 3 or 4 mm I think. Maybe a wee squirt of lub would help. Anyway I just grab that, fire it up, hold it for half a minute, maybe a minute, let it go, glove on and off I go.
So I've never bothered fixing the bar choke. I've always thought they are a bit silly anyway.