An AOA of 40 would launch you into the Sun, considering the light weight of the BSP4!
Here is my standard procedure:
De-orbit passing over the target base one orbit before re-entry.
Hold yourself level with the horizon with speedbrakes extended until you reach about 70 km, at which point I hold that altitude.
Enjoy a nice, slow, fire-proof braking maneuver in the upper atmosphere.
I gradually lower my altitude as I slow down to increase air resistance, but I still go slow enough to avoid plasma burns.
Then I just glide in from there. Long and shallow.