Hi,
Could you verify the MicroSD pin documentation posted on you web site matches the hardware implementation? I think I read that the CS data line in the SPI interface should be unique to the individual device and the shared data lines (MOSI, MISO, and SCLK) should be connected to the same pins of when using multiple SPI devices? Looking at the Tiny Circuits Micro SD shield documentation, I noticed that pins 11 (labeled SCLK) and 13 (labeled MOSI) are swaped relative to the documentation for the Nordic BLE, BLE St, WiFi, and other communications shields in the Tiny Circuits store. If the MicroSD documentation is correct, then I think it means the MicroSD shield is not compatible with the other SPI devices.
