What would be the best alternative during a dead-stick approach?
Attempting a tight turn, while low and slow, is an almost certain recipe for disaster.

Your first option of landing with a tailwind is possibly preferable - there is no inherent danger landing with a tailwind - it'll extend your landing, and is not ideal. However, it is much safer than trying to maneuver into a position with a headwind with only part of the runway remaining. And with a short runway to start with (if that was the case) you might not have enough distance to land safely anyway.

There is a third option, with the setup you describe, which is to completly disregard the (seemingly) obvious runway close by and look for a suitable area to land in front - a field, a highway, a beach - any of the usualy places you might make an emergency landing in the case of an engine failure.

(Disclaimer: My experience is with single engine propeller aircraft, but I am fairly sure the mantra of Aviate, Navigate, Communicate applies to all aircraft types. Really, in this situation its only the aviate that is relevant)