I’m OK with orbits which are essentially eccentric. Up until Kepler, the orbits were expected to be perfect circles. Then Kepler showed that they were elliptical. Then we found out they were basically elliptical, but eccentric.
It just seems to me — and maybe I’m wrong — that if ice buildup were to increase the eccentricity, I do not see how a return to relative stability would be achieved. I would expect greater and greater degrees of eccentricity.
It goes hand in hand with ice shelves calving. The weight of the ice forces the shelf farther and farther out to sea. The ice flows. Eventually simple strength of materials tell us that the shelf is going to break off. I’m always amazed at the doomsayers who seem to think it should continue to the equator.
Ice on land is different but the same. The sheer weight forces it to flow. Eventually another force, temperature, is going to prevent the ice from covering the globe. It might be interesting for scientists to study what affect the increase in freshwater runoff has on climate.
Ice build up does not affect orbital eccentricity, nor substantially affect axial tilt or orientation. An ellipse with an eccentricity of 0.0 is a circle. The solution to the two body problem in Newtonian mechanics is conic section: orbits are either ellipses (a circle being a special case), parabolas or hyperbolas. For bodies which are graviationally bound (specific orbital energy < 0) they are ellipses, for bodies not gravitationally bound (soe >0) they are hyperbolas. For the case of soe = 0, parabolas.
There is a really nice introduction to orbital mechanics, by Bates, Mueller and White, “Introduction to Astrodynamics”, if you are interested.