Hi megeegee,
You are indeed correct that there is an organisation with this focus, but it is a private organisation not related to Sanparks. It is actually referred to Eden to Addo. My girlfriend recently took part in the Eden to Addo hike, a total distance of 400km over 18 days - I AM SO PROUD OF HER!!!
It started in the Harkerville area (between Plett and Knysna) crossed 5 mountain ranges in the process and ended at the foothills of the Zuurberg in Addo. It is a "lazy" hike, meaning that you only carry day packs. Your main bags are transported in 4x4's and the logistics team does everything, from setting up camp, digging toilets, to cooking for you.
This hike is an annual event and is used to raise funds and awareness for this proposed corridor. I did not take part, but judging by the stories and the photos, it is an incredible experience and well worth it. Im sure if you google "Eden to Addo" you will find more information.
I hope this helps.
Kind regards,
Pat