2 circulars/shuttles might not be a bad idea
1 would take the route of the 14 from foot of the walk to commie pool and turn onto Newington and follow the 7s route back to foot of the walk.
The other would mirror a section of the 3 from Bernard place to haymarket
For the Leith Walk & Newington example the 7 and 14 routes are already reasonably short, serving quite useful termini, so it might make more sense just to strengthen these. Between Newington and Haymarket the 3 is joined by the 31, 33 and all except the Atholl Crescent area is covered by the 30 and 37 as well. Passengers have quite a wide choice at the moment so I can't see a separately numbered but almost identical route being a magic bullet.
Short workings are sometimes helpful to address crowding and definitely have their place but timetabling complications can mean they often just run empty. In years gone by the Festival season would see extra 41s between the city centre and Blackhall theoretically running in between the timetabled 41. But of course the normal bus would be delayed by 10-15 minutes anyway, and nobody would deliberately wait for the short working service. This often resulted in the normal bus being equally busy as before leaving the extra one lightly loaded.
I fully understand the frustrations with crowding and being unable to board the only service that goes to your desired destination because it is filled with passengers who had a choice of buses. However I wonder if these types of suggestions for new routes or shuttle buses may be better suited to the 'speculative ideas' thread rather than discussions on Lothian's normal services.