These are some very good thoughts. I often think about the continuum of body-mind and karma in this way.
Here the body-mind is now, experiencing and being the results of past karmas. For simplicity, we will call this state ‘A’: body-mind experiencing and being the results of past causes and conditions. As we experience these results and exist as these results, we generate all sorts of new causes and conditions, let’s call these ‘BCD’: new causes and conditions existing in potential form.
Technically, these causes and conditions would be described as being established by way of non-disintegratedness. They are not actively ripening, but they have not gone away. They are the sound of an echo before it has hit the mountainside–before it has hit your eardrum. What is that sound? It’s not a sound, but it’s also not gone: it’s non-disintegrated. These echoes are carried on the ‘mere I’, maintained even between lives. The ‘mere I’ is the misperception that there is a ‘real me’ who is unchanging, self-existent, and independently controls the body-mind. This ‘real me’ either pervades the body-mind, is among the parts of body-mind, or is somehow beyond the aggregates of body-mind. In any case, we have this misperception that our body-mind is controlled by this self, somehow existing within or apart from the aggregates.
So, here you are:
You are suddenly hit by a bus. All that remains of A dissipates, and B gets triggered. Now, you re-arise as a shrimp:
B-CD. There is a ‘Mere I’ seeing the shrimp body-mind ‘B’ as ‘MINE’. The continuum of mind is also carrying unripened karmas ‘CD’.
You start performing actions, creating further causes and conditions (not too many though, because you’re a shrimp):
You get eaten by a fish. B dissolves.
You re-arise as C-DE: you’re human again, and this goes on and on.
You accumulate many karmas as a human:
C-DEFGH. Death and rebirth. D-EFGHI. Death and rebirth. E-FGHIJ. Death and rebirth. F-GHIJKLM.
So, there is no unchanging essence or core that continues onwards as you die and are reborn.
Does this help?