Andre, to the best of my knowledge the inner core has been growing, just that, just growing. (I accept that its spin is not perfectly aligned with the mantle - that was never my issue - so please let's not go back there.) I thought I had made myself perfectly clear earlier; but I will reiterate for your benefit.
I find the notion of an inner core which undergoes cyclical melting and cooling ridiculous. This to me implies a growing and shrinking inner core! (I accept major events such as moon forming impact, could have melted (and shrunk) the inner core somewhat, but such events are not cyclical!)
I feel I must tread carefully here because some of your statements, such as the following, are not obviously incorrect (although I will try to show that this one is - given that by "variable" you clearly seem to be implying "growing and shrinking").
... variable inner core size due to solidification and core mantle friction due to precession differences of the inner core gyroscope and the mantle gyroscope...
Let's have a look at what an expert on this subject has to say: Don Anderson (http://www.gps.caltech.edu/~dla/Commentary-doc2.pdf )
The inner core is subjected to a variety of external stresses involving variations in orbital and rotational parameters, tides, gravitational tugs from the mantle, viscous drag of the outer core and electromagnetic forces. It may also generate internal stresses by thermal and chemical variations, anisotropy and cooling, and respond to these by porous flow, differential rotation, convection, and deformation and creation of material anisotropy...
The conventional explanation of the formation of the solid inner core involves slow cooling and crystallization. Since the melting temperature increases with pressure
the core will solidify from the center outwards.
A growing inner core is needed to power the current dynamo but rapid cooling may have
powered the ancient dynamo (9). The inner core may therefore be much younger than
the Earth. The heterogeneity and anisotropy of the inner core may help constrain its
apparently complex history.
So deformation of the inner core may occur by a variety of mechanisms, however, this does not necessarily mean that it can shrink. If a growing inner core is required to power the Earth's magnetic field, then a shrinking inner core would be detectable in the palaeomagnetic record (I guess it would appear as a drop to 0 intensity). There is no palaeomagnetic evidence to support this, especially at 100,000 yr periodicity!
So we have no evidence that the inner core shrinks, and you have certainly not proposed a viable geophysical mechanism that would allow for the inner core to shrink. The only geophysically plausible way to shrink (melt) the inner core is to either (1) provide a great
new source of heat, or (2) release a vast amount of pressure. If I were you I would either give up your wild goose chase, or if you're really convinced you're on to something, take a PhD in deep Earth geophysics, run some calculations, and (if you turn out to be right) get them published in a reputable scientific journal.