Since some OMs remember being other OMs, we imagine a single thread of continuity pointing backward.

I have a problem with the word 'imagine' here. Let's say that an OM is composed of the space-time slice roughly one second long and the volume of your brain wide. In this interval, the OM accesses neurons that store some particular memories, those of past OMs.
Why that happens? Unless you are a Boltzmann brain, it's because the state of those neurons has been causally originated from the state of the world in the past where there was another OM very 'near'.
Now the problem is that, having already identified myself with an OM, I could very well imagine of having been that OM who originated the state of my neurons, or the past OM of Britney Spears, whose influence on my neurons is negligible (ehrm... in a proper sense). I feel that calling both those instances with the same word is deleting a very important and cogent information.