Thanks for your kind help! This case and my mistake is solved now!
In case if someone finds this helpful,. this is what I made:
Didn't use any JTAG cable/adapter but instead installed openOCD to this same PI3. Then some JTAG wiring and successful programming to the Spartan6.
Followed this:
catleytech.com/?p=2679
Changing over to 40 pin flat cable,. short enough,..
Then, without powering down the MESA card, wrote bit file to user area.
