I think the Meadows is unusual in having one very decent direct path in Edinburgh though (and poor east west ones) .
MMW has a 50/50 split so park users can see there is cycle provsion. This sort of sets the tone for crossing Meadows quickly. I reckon I can use fairly quickly -watching out for children and animals of course.
The Jawbone Walk path I wouldn't generally use as I find the lights awkward and it appears to be too busy - plus the signage (right or wrong) discourages me.
Of course Argyle Place is awkward too with cars having the best line.
I use the green Sri Chimnoy path to do some practice rides and I do ignore the 'No cycling' painted at the East End near the WCs. (So I'm inconstant)
You usually find a council van parked here. Also some parents drive their kids to park across 'no cycling' signage.
The green path is not marked with anything so I consider legal to cycle (carefully)
Maybe I'm part of the problem - though my 'law breaking' is only on Sunday mornings before 11am.
I do recognise that people have right of way / shared use etc.