Thanks for the tip - I attached and external HDD, pointed transmission’s download folder on it and now everything works perfectly - average download speed 8 MB/s, no drops in speed and system (incl. Kodi) works perfectly in parallel.
I would highly recommend on adding a comment at the Transmission’s page in App Store about this - I would say that an external HDD is a must and SD card is an absolute no go.
Thanks once more!