I have a (maybe silly) idea .. replace proof of work with proof of time. Instead of mining, run some time consuming process, which cannot be done faster, after which the proof of time will be the lottery ticket to win the block reward and secure it, too.
For example, imagine a device which is natural random number generator - let say a radioactive decay material with a beta particle detector (classic may know that a sufficient hot cup of tea may work, too). The detector will try to search for a rare event in the incoming stream of detected decays, like special sequence of delays between each detected particle. Or, the device may wait for all 2048 molecules of argon to collect at left part of some volume (unlikely, but with the Maxwell's deamon help, possible). Or, waiting for the special mutation of bacteria with large prime number encoded in its protein. Or, those who really understand quantum mechanics (yeah, I mean those 10 people on Earth), can bring up something even better.
Of course, such a device must be self-contained, where the part of testing the work is integral part of the device, cannot be cheated on (like faking the generator). This is the hardest part of the idea to implement and I know it. Speaking in words of one-way functions, the device must somehow report found solution, and somehow prove it, to avoid faking. Simulating the process on any fast computer must not help to find it (nature and its atoms are faster).
Such a device will silently, with minimal energy, run its lottery and its user can only wait (or collect more devices) until a possible solution is found and block secured.
As I said, maybe silly idea.
Fails the feasibility test and when you look at how to prevent fake readings you run into a brick wall and can't describe further.
Not to mention that most of what you describe varies by observer and thus can not be verified by other observers.
