Well I just caved and decided to file down the pin with a file with safe edges. I attempted to remove it, and it ended up pretty mangled. The bearing is in and everything is back together. I tightened the pre-load nut as good as much as I thought was possible without it locking up. I just had some 20wt oil in the bearing, and it was a bit loud I only ran it for the short time in the videos. The top portion of the babbitt bearing cap is slightly smaller in width than the babbitt in the main spindle casting, I am not sure if this is how it was from the factory, or if it was due to wear. When I had it pushed slightly forward and had a gap on the side of the spacer/gear/pre-load nut there seemed to be more friction due to the spacer only bearing on half of its diameter. So I decided to push it back and I was able to tighten the pre-load nut slightly more and now have a very low amount of end play. The only problem is that now the thrust bearing is only bearing on the babbitt over half of its diameter and now it slips some times. I think If I measure the gap with feelers and place a brass shim I could increase the friction on the bearing side and keep it from spinning. I wasn't sure what the appropriate lubrication was, and I didn't want to pack it full of grease and then have to soak it in a solvent again to remove it from the balls.
How can I post videos? It says that the files are too large, so I tried to put them in a zip folder and it says that it is too big to post. Let me know how to upload videos so you can hear the sound of the bearing
Also I found someone on a facebook group that had just gone through the babbitt headstock of their Atlas 10" to get the play out of it. I noticed that he also had the stamped steel change gear cover that was only on the 1935-1936 models. I asked them if they had had a ball thrust bearing or just a steel spacer and surprisingly he just had a steel spacer similar to my lathe. I remembered how you didn't have parts lists/diagrams for the 101.07306x models without back gears. While his did have back gears, it was of the same generation as mine, so I wonder if the ball thrust bearing might have been something that was added with the update in 1937 when they cast change gear cover, and reinforced tailstock were added. Here is the pic from his facebook post.