I have a supplier using the DK-DEV-5CSXC6N. Using the on-board USB-Blaster circuitry they can successfully run debug sessions on both the HPS and the FPGA. However when using an external USB-Blaster not so much. They mostly see timeouts in DS-5 when the debug sessions is waiting for the ARM cores to become ready. Sometime they just cannot connect to the board. We need to get this method working (i.e. using the external blaster) as our production PCB only has the JTAG port, not the USB port and the associated Blaster circuitry.
USB-Blaster II (https://www.digikey.com/products/en?mpart=PL-USB2-BLASTER&v=544). My supplier has two and tried both getting the same results with both. They tried a 1M clock with the same result. The supplier stated "I believe we tried changing the speed at one point and it was not successful. I just tried again and once again have not been successful. JTAG speed is reporting back at 1M".
Based on your description, it seems like the USB-Blaster II is having problem as the debugging tools and USB-Blaster connection was working using on-board usb blaster. Can you try with another USB-Blaster II?
Also, can you try TCK frequency at 6MHz. 1MHz is too low and it might not working sometimes. Also, i have attached the method to configure the TCK frequency at link below, just in case you need it.
Apologize that I cannot open the image file. Maybe can u attach it on the forum?
Can you check the following?
 Change the switches and jumper to default position.
 Check whether if the HPS is in JTAG Chain when using USB-Blaster II? To check, simply open SoC EDS Command Prompt and type "jtagconfig".
 If it is on the JTAG Chain, try to program the board with USB-Blaster II.