I found some references in Sportsman's Arms and Ammunition Manual and Complete Book of Rifles and Shotguns both by JOC. On p173 of my Complete Book, there are cross sections of six bullets, with one being the 180g Bronze Point. It appears the jacket is the same width from the cannelure to the tip, maybe just slightly tapered as you get to the top, not much if at all. If it is not tapered or maybe just too thick to begin with, then that might explain comments about it not opening up.

O'Connor states in Sportsman's Arms p44, "I have respect for the Remington Bronze Point bullet in 150 and 180 gr. for the .30-06. I used the 150gr version almost exclusively from 1927 to 1934. It shot flat and accurately, and its action on game was very reliable. In construction, it is a hollow-point bullets with a bronze wedge set in the cavity to retain the spitzer shape and to open up and split the bullet when resistance was encountered. It is a curious circumstance that those little bronze wedges usually penetrate more deeply than any other part of the bullet. I have picked many of them from under the hide on the far side of large animals."

1927 to 1934 was a long time ago for a "tipped" bullet. I didn't realize they made them that long ago. It's possible that Rem. changed the manufacturing processes many times throughout their production, effectively resulting in "different" bullets.

I think I'll put them into some bound papers and take a look.