Might be best for someone not tied to the KF staff to take over. I have little doubt that Woods and Parker have the stuff to become head coaches, but they might want to make a name for themselves at an FCS or MAC school and get a fresh start.
Best-case candidates are Bobby Stoops (he may or may not be interested - and he just turned 60, so his shelf life is limited if he wanted the job), Mark Stoops, and Chris Kliemann. Candidates of color will likely be interviewed as a formality, but a lot of them probably wouldn't have much serious interest because even if the whole Doyle fiasco never took place, it's still a tough sell for lots of reasons: The weather in IC is mediocre-to-crappy from November through April (a lot of black and Hispanic coaches come from the South and West where the weather is generally much milder in late fall and winter), it's very much a college town at the end of the day and doesn't offer the same amenities a city like Chicago does, and the last non-white coach Iowa had in a money sport bolted after just a few short seasons (and IIRC, Raveling said something to the effect that even as a black guy, it's tough to recruit black talent to IC).