Right now, the properties of the pre-determined re-entry profile are well
known and the shuttle's guidance computer is well programmed to handle it,
allowing shuttle to de-orbit at the right time and reach the runway vicinity
at the right altitude/speed. They even know prior to de-orbit burn the target
runway. Fairly routine stuff.

Ok, lets say that there was a problem with tiles and that they decided to
attempt a very different re-entry profile to protect the damaged side (at the
expense of other areas). Could the re-entry program be modified with a new
re-entry profile while the shuttle is in orbit ?

Could the guidance computers be programmed to perform the initial/different
re-entry which would bring the shuttle to a random location at a specific
altitude and more or less random speed, at which point ground could decide
which runway to target and re-load the computers with the necessary info to
reach that runway ?

Or are time constraints such that they would really need to program the full
re-entry in advance without any time to change anything once re-entry
interface has been reached ?

Is knowledge of re-entry aerodynamics such that NASA could quickly simulate a
very different re-entry profile yielding information that would allow NASA to
program the guidance computers to de-orbit at the right time and perform
whatever manoeuvers (skips, turns etc) and bring the shuttle out of re-entry
interface at the right location and altitude to allow landing at the right
runway ?