By all means have a trigger job done. Frivolous U.S. law suit have caused the manufacturers to sell their firearms with poor triggers. Even rifles costing a whole bunch more than your Stevens. Mind you, 1.5" isn't terrible for an out of the box rifle. However, you have to work up a load for any rifle, not just pick one and hope. Your rifle will likely prefer light bullets(the rifling twist is good for light bullets) like your 55 grain bullet, but you have to work up the load. H380 is given as one of the accuracy loads for a 55 grain jacketed bullet in my old Lyman book. (35.0 to 39.2.) So you're close. Make sure all the stock and sight screws are tight, then do this to work up the load.
Beginning with the starting load given in your manual, load 5 rounds only. Go up by half a grain of powder, loading 5 of each keeping them separate until you get to the max load in your manual.
Then go shooting. Shoot at 100 yards, for group only, slowly and deliberately off a bench.
Change targets between strings of 5 and allow time for the barrel to cool.
When you find the best group, sight in.