I think all you have to do is connect the Data Out pin of the SD card holder directly to the MISO header, and cut the trace from the level shifter gate output to the MISO header. The card itself will behave properly, and release MISO when its CS is not selected. If your microSD module looks like mine, these pictures demonstrate what to do.
I should add that the Adafruit microSD card adapter does it this way, and it plays well with others. A 3.3V output on MISO from the card will be received as a high by a 5V processor. Actually, there was no point routing MISO through the level shifter in the first place since it just shifted it from 3.3V to 3.3V.