I don't know about out shooting the Baretta because I don't have one, but I have a Taurus 99 and have absolutely no problem shooting it in it's stock form, other than having pacmyer grips on it.
I have had this one well over 30 years and after I tuned the adjustable sights to my shooting habits, it is extremely accurate. The trigger has never been a problem for me.
I consistently score 100% on my CHL shooting renewals. Maybe I just don't know what a good trigger is on a pistol, but I do have a few others that I do know what a bad trigger is.. AMT, Keltek,,,,, lol..
I even like the trigger pull on the old Taurus better than my
XDm9.
Sorry this doesn't answer any of your questions. I just wouldn't even think of "fixing" it.