I'm pretty sure I've heard both "Shinbone Al" and "Round the Corner Sally" from Theresa Tooley (Shellback Chorus, UK and Mudcat's "treaties"). Heard other people sing them too, so I'm not sure what you're basing the "rarity" rating on - it may be that (at least until recently) this area (NW England) has been very well served with shanty festivals (particularly Lancaster/Glasson and Liverpool, with Hull just across the Pennines) and I've had a chance to hear many excellent shanty choirs and singers, both local and from Europe and USA, so it could just be accident that I have heard these songs and you haven't come across them. Another excellent local resource for shanty and sea-song material (CDs, tapes and books) has been the Chantey Cabin.
Liverpool's Stormalong John used to work with Stan Hugill and continue to keep many of his songs in their repertoire, many of them not so far on CD. Just looked through the listings on the Chantey Cabin website, but can't find the shanties you've mentioned.

Ross