If you are mining new block and secure some transactions with it then we say that these transactions belong to that block. If you say that they were part of previous block but wasn't secured by it then this is just a game of words, because you are that guy who secures them and you deside which transactions will belong to previous block, not the one who mined previous block, so it is still the same as if you added these transactions to your block. Each block includes hash of previous block, therefore currently all previous blocks are used for seed.
You would still attach the PoW to a new block with new transactions, your map seed would just reference older data. Yes, when you solved this map it would do nothing to confirm the integrity of those transactions at that time (instead adding confirmation only to the blocks up to where your seed block was) but in the next N blocks when someone else solved against your block (or any block after it) it would serve to secure those transactions. This is why I say it would require N times as many confirms to be sure of a transfer.
(EDIT to clarify: Really I think there are a
lot of problems and potential problems with this approach anyway, particularly related to the extra confirmation delay and "S.E. attacks," so it should probably be considered as a nearly-last resort approach. I think something based on proof-of-activity(/stake) blocks is likely a much more viable solution.)
You don't need to change time, you can just change your address for coinbase transaction. With some other tricks you can have even more insanely larger set of possible maps.
Good point. Still finite, but for all intents and purposes it might as well not be.
Yeah, it is
exceptionally secure. And you can perform 99% attack any time you wish, sounds very secure.

Yes, granted, right now we (botters) "own" the network, and there are only quite few of us. My point stands, however. The network would be difficult to attack by anyone "not us" now. Presumably there will be more and more of "us" with each day, both adding strength to, and decentralizing that ownership of, the network.
Remember that physics is calculated not only while playing but also when other nodes check blocks for proper proof-of-play.
Right, just adding computational effort to the path is not a good solution.
Right now I can check about 60 blocks per second in one thread on my Core i7-3770.
OUCH if this is just PoW checking time something is very wrong, then. You should get significantly better performance than this.
With 4 threads I will probably be able to check 240 blocks per second but many people have much slower processors. With your proposal physics simulation will become much slower and to really harm the bots we will need to make it at least 100 or 1000x slower. This will make block checking very slow, on some computers it will take several seconds to check one block, some probably would check new blocks slower then they are generated, inital synchronization with network will take days or even months, botnets will perform spam attacks sending a lot of invalid blocks and nodes will use 100% of their CPU time to check these blocks.
Yup. Not to mention the "clincher" here which is that the bots could simply run their solutions without this "added legwork" and then re-run their path against the "full physics" once a solution is found to verify that it will be accepted by the network. This would just hamper normal users a LOT and the bot heuristics very very little.