I agree that responsible cycling is required. I avoid the area when it’s busy and if there is a walker approaching, i’ll either slow down to a crawl or stop to let them past.
Stay away from the radical road and only use the path that goes up through the middle for ascent. There are loads of paths that are hidden with very few or no walkers. It’s all on narrow well worn single track and IMO not adding to the erosian or creating new paths.
Couple of recommendations:
For ascent to the pond at the top, instead of riding up the road, head to the small car park at the Meadowbank end of the park. In the far corner there is a path that takes you all the way up to the back of the pond at the top of the hill.
From here there are various options but an easy one is to cycle round to the roundabout at the bottom of the hill near the commy pool. head up the hill on the left (if your heading towards Hollyrood, the big hill on your left). Here there is narrow and fast singletrack that takes you all the way to the Scotsman building. Where you can do another loop on different tracks.
These sections are very quiet as they are “out of sight” of the masses and i’ve never seen another cyclist on these paths.