@Oblaaspop
You are right about the STOP in Airbus SOP however the start+taxi is PF's job (CM1 or CM2) ... also crosswind shouldn't be an issue in a company that only takes experienced (4000+, err 2500+ ... err ... cadets) pilots.
Techlog is company's decision so no reason to upset anyone (never liked paperwork).
(55t or not ... still b***sh*t)