I don't have much in the way of those fantastic stories that you shared. Whether or not they fit into Dick's explanation is for you to decide.
My 'experience' with synchronicity is on a much smaller scale that has more to do with interesting tie-in's with what is happening at the moment. For example, a few times while reading the exact same phrases in the paragraph were repeated by someone in a room or over the television, etc. This type of incident happens frequently to me.
But, I should be a little more specific. It isn't just that they happen out of the blue, they happen at specific times. Namely, when my studies heat up and especially when I gain (or I perceive) new insights. At these times I have noticed an increase in synchronous moments.
The strange thing about synchronicity is that it doesn't seem to be intelligent driven (perhaps random driven to the skeptics *smile*). Rather, it seems that synchronicity occurs here and there for no apparent reason. I've thought about the possibility of an esoteric message (e.g., I should buy Intel today), but unfortunately I haven't seen any reasonable justification for assuming this to be the case.
I think we should be skeptical over synchronicity of this concept, however let's take Alexander's proposition that math is everything. In such a context, would it be so unimaginable that remote systems come into sync due to some logical relationship? Synchronous functions, I believe, are studied in mathematics and I wonder if those functions have a much wider application then physical systems.
Without more understanding of the metaphysical nature of the world it becomes very difficult to guess how such relationships (if they exist) can influence human affairs. I still have my eyes peeled to studying this pseudoscientific phenomenon.
Warm regards, Harv