From my mathematics background, I do know some things:
- Chaotic systems can sometimes oscillate between two (or more) quasi-stable points.
- The climate of the Earth is (at least to some degree) a chaotic system.
It is possible that the climate oscillates between ``warm'' and ``cold'' on a millennial scale without any external driver.
- Long-term behaviour of many-body systems is difficult to predict with a finite number of perturbation terms.
- The influence of the Moon and all other planets on the Earth is calculated using perturbation theory.
It is possible that there are millennial-scale variations in the Earth's orbit that have not yet been calculated.
- Ice cores do not directly record the temperature.
- The temperature at the time the ice was deposited has to be estimated from various proxy data (concentration of various gases in the ice, etc.).
It is possible that these models are wrong, and there is no millenial-scale climate variation - only a millenial-scale ice deposit variation.
Of course all of these are very tentative, and I am fairly certain that the last possibility is false.
However I consider all of these possibilities more valid than your solutions.
What you are proposing:
- We do not currently have a quantum theory of gravity.
- However to fit in with the Standard Model, gravity must be described by spin-2 gauge bosons.
- Your model of gravity (the ``archimedes screw'') is not a spin-2 gauge boson.
For your theory to be correct, the Standard Model must be wrong.
- In General Relativity, gravity fields are not self-interacting.
- In General Relativity, gravity fields can be constructed from a superposition of point sources with locally inverse-square dispersion laws.
- Your model of gravity suggests gravity is a non-conservative field that cannot be constructed from point sources.
For your theory to be correct, General Relativity must be wrong.
I, personally, am not convinced that a qualitative explanation for millennial climate patterns (drawn from a few ice cores), unexplained ship and aircraft losses (drawn from a few non-weather, non-human-error related examples), anomalous spacecraft phenomena (that only affects some spacecraft in some situations and does not seem to be repeatable), and various eye-witness reports of bizarre events (but otherwise unnoticed - or at least unreported - by any official presence), is worth throwing out the two most successful theories we have.
Make no mistake: the Standard Model and General Relativity are wrong or at least incomplete. But whatever replaces them must reduce to each of those theories in the appropriate regime, and must reproduce the successful predictions of each of those theories.
It is not clear that the Standard Model and/or General Relativity cannot - without any modification - predict events like the ones you list. All calculations on many-body systems involve approximations (treating external sources as weak perturbations, for example) and simplifications (ignoring some external sources).
It is quite possible that if we improved our approximations, and reduced the number of simplifications, our existing theory would predict the events you mention.