Just a thought, try tapping the charging handle forward to ensure it is fully into battery. You can do a search for "Benelli click" and you'll see a lot made about a rare problem that in my opinion has been blown way out of proportion.
The trigger job would be high on my suspect list, but it sounds like it is functioning by starting the firing sequence as it should. It makes me think perhaps the spring could have broke or something is in the way blocking the firing pin mechanism itself which is in the bolt. I'd field strip the gun and take the bolt apart and check it all out for cleanliness, then the firing spring spring. If all that checks out, you can drift out the pins to the trigger pack if you can't see well enough and inspect for anything broken or pins/springs, etc not in place.
In the end, if the bolt looks good and clean, I'd call them back. If they don't want to offer to look at it, make them a deal. Remind them of their Mission statement to stand behind their work.
1. You send it to them, and if they find another issue other then the previous work they have done, then you pay for the work they do. Make them document exactly what the did find.
2 If they don't want to do that, how about if they agree to pay for it if you take it somewhere else and it turns out to be the trigger and they owe nothing if that isn't the issue.
3. Get it fixed somewhere else and if they determine it is caused by the trigger job and Cole's won't stand by their work, post the report on sites like this so others know to stay away.