I would strongly advocate for the enclusion of a BP cuff and stethoscope. Doing mountain SAR, when my bag was culled routinely to eliminate frills and unnecessary items, I, and all my colleagues who were suitably trained, toted cuffs and scopes. Especially if a long interval has elapsed between first contact and arrival in the ER, the recording of vitals will be really useful for downstream care.

You are recording more with the scope than just BP - cardiac and lung conditon are pretty important as well. It looks like you are contemplating a combat situation, what with the TCCC, and tourniquets. My experience, dealing with the kinds of traumas associated with folks coming to grief in the wilds, never involved the need for a T, but we always tracked vitals. Both are a really good idea, but, if push came to shove, I would keep the BP and scope.