Compiling relevant literature for a meta-analysis. See https://sites.google.com/site/publicationsericgilman/home/reducing-elasmobranch-shark-and-ray-bycatch-in-pelagic-open-ocean-longline-fisheries
From experience, I would say that bait type and hook dimensions are two key factors in determining catch rates, and soak time will have a strong effect on haulback disposition. I'm sorry I can't provide a reference for you, but have you found:
Favaro and Cote. 2013. Do by-catch reduction devices in longline fisheries reduce capture of sharks and rays? A global meta-analysis. Fish and Fisheries.
Spanish colleagues at IEO (look at Macías at reseachgate ) can provide some information. One document presented at SCRS of ICCAT is : https://www.researchgate.net/publication/269105455_Influencia_del_tiempo_de_permanencia_del_aparejo_en_el_agua_sobre_la_captura_accesoria_del_palangre_semi-pelgico
Article Influencia del tiempo de permanencia del aparejo en el agua ...