Alright, now how does the rest of the network measure that a block has been passed "a long distance"?
What's stopping me from setting up two separate looking nodes on the same hardware and having it pass the block back and forth between those two nodes? Do you have to accumulate signatures from many different nodes to prove block validity? How does the network know when you have enough? Does it have to be signed by 51% of the network? You're opening yourself up to Sybil attacks like crazy it seems to me.
How does the rest of the network measure the "distance" between two nodes to verify they are far enough apart? Does it measure their connectivity in the network? What if those two nodes, running on the same hardware, just choose to connect to different other nodes - one connects only to nodes around the world and one only to local nodes.
And once again, how does this provide incentive to de-pool, or remove the pools mining power from the process of writing transaction history? The pool that is performing the 51% attack doesn't need to release the blocks in a way that looks like they're coming from that pool - just making 51% attacks harder to find. They can find a block, and decide not to release it to anyone, just shuttle it to a colluding server which is say "hey, look at this nonce I found that works if you publish it with these transactions", then that server publishes the P-o-W and it looks like it comes from the remote server, not the pool. The shuttling doesn't have to occur over the bitcoin protocol. Then the remote server releases it to the network instead - to the rest of the network it just looks like that server was a little (milliseconds) slow to publish - which could be due to literally anything, perhaps the router it's behind got backed up, they have a slow internet connection, etc. So if you then enforce that the blocks have to hit the first node within a certain amount of time after their time-stamp, then A) you have to make sure that the network has synced clocks, which is really really much more difficult than most people imagine, getting even second-accuracy on the clocks can be a challenge when you have to deal with competing traffic between servers (how accurate is your clock:
http://time.is/, mine was 16 seconds behind, is that an acceptable difference in time? More than enough to shuttle a block around the world for release), and B) you are punishing people who have slow internet connections because they simply can't publish the blocks they find quick enough - leading to people buying massive hardware and massive connections and encouraging pooling.
So what if you include a signature with the timestamp, and say that that has to hash out correctly too (so you include that signature in the proof of work). Then you're back to trying to verify identities. Which could work, over a long time - you could use something like a Fawkes signature protocol inside the bitcoin protocol that built trust in signatures over time - the more a signature is used and verified to come from the same place over time the more it's trusted to not be used in multiple places. But, this actually encourages the same servers to publish blocks over time, otherwise everyone is at zero trust.
So, I think that your solution is actually encouraging big/pooled mining:
You need expensive hardware to produce accurate time-stamps, which the lay-person can't afford.
You need expensive hardware and contracts to have fast internet, so that the network doesn't accuse you of purposefully holding a block back a certain amount of time or attempting to shuttle it elsewhere for release, which the lay-person can't afford.
You need repeat blocks from the same person to build up trust in signatures over time, which makes it harder for someone who is just solo mining a block every now and then to get his block accepted in the network.
You still can't stop someone from setting up two servers (or N for that matter) which look very different to the outside world on the same hardware and using those to collude against the network - something a pool operator would have the power to do.
