I replaced a hinge pin in a LC Smith FW with the Brownell tapered reamer and pin supplied by them. My frame was annealed. Ream the hole with the barrels installed to the frame and you get a perfect tight fit. One thing to consider when pushing out pins from frames like the LC is which way the taper goes. You want to push on the small end. The LC Smith also has two small dowel pins holding the pin from moving and are on the fore end pivot surface. I found out the hard way and sheared them off. Other guns may have these or some variation and they can be difficult to see. Look at this surface on your LC and see if you can see them. It could be difficult drilling these pins if the frame is hard. Maybe a cobalt drill bit would work or one of the other space age bits. Some of the other higher Quality guns have the screw off caps to make hinge pin replacement easy with a straight pin. Those with machined in pins need the hook welded to tighten them up and there was a nice post about that here a couple of months ago.
