I'd ask the gunsmith what is causing the bullets to hang up.

Lots of things go wrong when you tell the professional what you want them to do about your problem rather than just telling them what your problem is.  Yours sounds unusual so I'd get a second opinion.

 

My first though would be the ammo itself. If the hangup is that the rounds are not fully seating I would check that the bullets are not seated out too far. Also would check for proper sizing of the bullets and if they were ok would then try a Lee factory crimp die. Check for high primers too. You don't mention the brand or model of pistol or if the ammo is factory or reloads but I would avoid the reamer until I knew for sure that the chamber was the problem.

 

It's a Para Carry 9. Common problem with lead bullets...the throats are tite. A jacketed bullet is fine. Lead bullets are larger in dia. .355" vs .356 or .357". I need to get it reamed a tad or will only be able to shoot jacketed bullets. I got  a lot of loaded rounds I cud be shooten if I could get my hands on a reamer reasonable.
That's my story and I'm stickin to it !!!!
ps: pistol shoots real good anyhow.