Just because something is temporally extended needn't imply that every temporal slice of the extended thing is identical to every other temporal slice. Differences between one slice and another would represent change in this this kind of scheme, and we obviously change during the course of our lives. (That introduces the problem of how to define personal identity.)
I am not saying that every part is identical to every other part, or that it is a requirement for composite objects. Certainly such a view would be clearly false because that would mean that there can be no objects with heterogeneous parts.
I am merely saying that the whole, which is identical to the sum of every part (but not identical to each individual part) should itself have the sum of the experiences which every part has. That is, if a time slice has experience x at T1, and another one has an experience y at T2, then, as the being who is composed of both time slices, I should have an experience x at T1
and y at T2. In other words, I have them both together.
Assuming that we are conscious throughout our lives (which isn't likely to be true)...
Even if that weren't the case, we are certainly still conscious for a fair amount more than a single instant, so it doesn't seem to matter for the purposes of my argument.
... we should probably say that our consciousness at time T-1 is consciousness of T-1, while our consciousness at time T-2 is consciousness of T-2. So we can say that our time-slices are experiencing throughout, but only experiencing the time in which that particular slice resides (plus accumulated memories).
This probably has more to do with P2. than P3 IMO. From the looks of it since you don't seem to be disputing what I claim to be experiencing (or really not experiencing) as a conscious subject and are instead focused on what we should be experiencing.
In any case, I think your objection is missing some context. Sure a consciousness at a time has conscious experiences of that time, but what does this say for a
temporally extended spacetime worm that is the sum of multiple consciousnesses at multiple times?
Maybe I'm not understanding the distinction between worm-theory and stage-theory properly. It's conceivable that my amendments to your premises and my interpreting personal identity in something other than a strong logical way has moved me towards being a stage theorist and I'm actually conceding your point without realizing it.
Sorry if my explanations aren't clear enough. The wiki on perdurantism distinguishes between both views, so perhaps you can check that out for a quick reference.