Supernova/cosmic ray energetics also play a constraining role in this discussion, with both Ramaty, et al. and Parizot & Drury observing that there is an underproduction of Be (by over an order of magnitude) in the early galaxy if most supernovae explode in the average ISM.
Cosmic Ray Origin, Acceleration and Propagation
Only in the cases CSM1 and, more apparently, in the CSM2 case there is a slight underproduction of luminous white dwarfs.
Monte Carlo simulations of the halo white dwarf population