I would predict that most reducing agents will come from the convex face of your molecule. In this system it might be really difficult to get the other diastereomer because the other face is so significantly hindered. If sodium borohydride gave some reasonable level of selectivity, my guess would be that one of the Selectride reagents would give the same major product, but in a higher ratio. I suspect that two of your stereoisomers are resulting from epimerization of the stereocenter next to the ester in the reduced product. It might be very difficult to control that.
In simple systems, Selectride definitely does give axial alcohols when it is favorable. For example, consider the reduction of 4-tert-butylcyclohexanone. Small reducing agents like LiAlH4 generally give mostly equatorial alcohol (92:8 e:a), whereas large reducing agents like Selectride give mostly axial alcohol (7:93 e:a). See: Brown, JACS 1972, 94, 7159.
One other system to consider is the Noyori Ru-BINAP system for hydrogenation of beta-ketoesters. As I recall, it is selective for the reduction of beta-ketoesters over other alkenes in the molecule. You might be able to squeeze some selectivity out of the system with a chiral ligand as well.