Don't know about a trigger job, but there was a company at one time that made replacement triggers for Remington 870, 1100, and 1187's. They made those guns shoot much better on the slug range.
I've got one of the old Win. NWTF edition pumps and the trigger was mondo strong, I tore it apart to give it a good clean'n and while I was in ther I done a little work on the sear, it helped a lot.
But to be honest I would take it to a smith to get it done, a good gun smith will do it rite. I just about over done mine because I didnt know a better way but was able to fix my mistake.
Lol! Yes thats what Im trying to avoid. I definitely dont want to over do it. I have a tendency to do that when I do stuff like that myself. I appreciate the help.
You can get the 870 police trigger assembly from Brownells. It is a little better put together and honed up a little bit better. It costs about $95 and is a Remington OEM drop in unit.
They can make it feel much better, but the trigger blade still feels awful. The replacement trigger has a nice wide, smooth blade. I guess you might be able to find a trigger shoe for the original though.
Don't know how far you are from Paducah KY but Lynn at Paducah Shooters Supply has done some trigger work for me before on a .22 and a .300 win mag.
If it can be made better he is the man to do it.