Hey, I never got around to updating this thread. I managed to bank out that tube from the frame, and I did install the
Shimano BSA Krankboks, 68mm (122.5mm version) I bought. As I feared, it was too wide, but I just accepted that, thinking that it was only a matter of aesthetics.
Then I left the bike alone because I also needed to change the freehub -- it took a long time to arrive and I had to focus on other things.
Now I finally got around to putting everything together and it rides great, but! I noticed that when I roll the bike back (only when I roll it back, the freehub is installed properly), the pedals turn back by themselves. When I do that having the chain on the biggest cog of the cassette, it goes out to the next cog by itself. If I lift up the back wheel and pedal backwards, it's the same story: when on the biggest cog, it goes out to the next cog out.
Eventually, I figured out what was happening. It's related to my new bottom bracket being too wide, as I initially suspected.
Bottom bracket too wide.
What's happening is that the overwide bottom bracket is causing the chainring to be too far out in the direction shown by the arrows in the picture below. This is resulting in a misalignment between the chainring and the cassette. It's hard to see it in the picture, but the chain is not centered in the chainring.
Chainring too far out
Ultimately, the result is the chainring pulling the chain out when I pedal backwards, as shown mid-action in the picture below.
Chain being pulled out from the big cog
I think it's all better illustrated in this final image:

I had originally thought that the derailleur needed adjustment, so I went through the process today until I discovered the real issue. Due to the nature of this misalignment, the pedal thankfully doesn't move when I'm rolling the bike forward or when I'm coasting. Most importantly, the chain doesn't automatically hop to the next cog under any circumstances while riding the bike. It's all as smooth as can be.
So now my question: Is it worth changing the bottom bracket again? Could this misalignment be causing any damage or be dangerous in any way?