refactor init codepaths

[oscardssmith]

Currently the process of init goes through a kind of crazily convoluted set of dispatches that initially existed to allow DifferentialEquations to hijack the default solve without causing method ambiguities. Now that we've moved to a model where this complexity isn't necessary, it would be good at some point to see if we can simplify the init->init_up->init_call->__init dance.

[ChrisRackauckas]

The main purpose of it is because we cannot differentiate keyword arguments in ChainRules, and so there are some parts of this specifically to handle the differentiation rule definitions.