I’m in Peebles and have lived in Innerleithen as well. The track from the cairn does eventually head back down to the trail, I’ve only ridden it once, while the descent was being built. It did get pretty wet and boggy towards the end and joins the SUW at the circles view point.
The other trail, at the SUW crossing was the way the XC used to go before the fast jumpy descent was built. It was a climb back up to join the wet boggy trail mentioned above. We always just used to fly down the SUW to get to the circles though.
As for the proper riding spots, there is a warren of downhill trails from the first and second fireroads. Most of these are rideabl on an XC bike, Iride most of them on my hardtail. The gold run, Cresta run and Make or Break are the ones on the map but once you get into the bottom section there are many options. Some do end up and drop offs (Matador), so be careful on your first run.