Shifters/brakes won't fit on bullhorn bars I have a KALLOY UNO HB-005 580 mm handlebar and a shifter with brake combination, Shimano Alivio ST-M310. I have a Sora derailleur and crank set. I got as a gift a bullhorn Origin8 Bully Bullhorn 6061-T6 Handlebar 400mm wide 31.8mm clamp. 

The problem is that the shifter's mounting ring is not enough wide to get on the bullhorn at all, I can't imagine how to put on it and if I manage the first centimeters, than there is a corner. How can I fit the shifter/brake on the new bullhorn or do I have to change the shifter system?

If only the mounting ring can be changed I would be happy. I opened the sifter but the bolt which holds together the brake lever and shifter is blocked mechanically (doable). Is there another brake lever that has a wider ring and can be replaced with the current one, so I can keep the shifter?

Edit 

I measured the old and new set:


KALLOY - 22.20[mm] 
Origin8 - 23.88[mm] 
Shimano Alivio - 22.38[mm]


Update

Would  it be a structural integrity problem, if I grind 1-2mm of the inner wall of the mounting ring?
I would advise against the grinding idea.  You might be okay if there's enough meat left on the ring, but these are part of your braking system, you really don't want that to fail.  Imagine an emergency situation, or even an intersection at the bottom of a big hill.  You squeeze the levers hard and the mounting rings break, your brake cables go slack and you can't slow down or stop.  Even assuming only one ring were to break, you'd have maybe half of your stopping ability remaining which could easily lead to injury (or worse).  The breaking of the ring could also startle you enough that you lose your grip on the handle bars.  Not worth it.