Combining BSP/GJKEPA/PGSLCP algorithms into a Game Loop

 I want to do the following;

• BSP offset as described by Melax in his paper for environment collisions.
• GJKEPA, or SAT for object on object collisions. 
• Use collision response formula for bouncing objects. 
• Use PGSLCP solver for sliding rolling objects. 

PGSLCP solver allows small inter-penetrations, which are corrected using Baumgarte stabilization.  This means I don't have to subdivide time intervals every time a collision occurs.  This works well with GJKEPA and separating axis, but BSP offset returns the exact time and location of the first collision.  BSP offset requires subdivision of the time interval, because if the object falls through the floor an infinitesimal amount the contact will not register on the next frame. My question; is BSP offset incompatible with PGSLCP solver? 

Edited January 29Jan 29 by Richard Baker
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