Hold on while I try to correct some nits in what Bertie said and see
what happens

Bertie the Bunyip wrote:
Nope, the wind is going to help you in almost every way if you're
turning back.
[ many good points supporting this assertion, but... ]
also, your best LD speed is going to occur at a lower
airspeed,
Well, technically, your best LD speed is related to angle of attack, and
not the groundspeed, so that won't change. Your best glide speed
certainly will be less...

There is no inertia involved in making a downwind turn. None.

Here's why I wonder about that. Let's suppose 65 KAS before and after a
180 turn from a 10 KT headwind. OK, before the turn, your groundspeed
is 55KTS and after the turn your groundspeed is 75KTS. Your intertial
frame of reference is tied to the g/speed, not the a/speed. So -- the
kinetic energy of the aircraft and contents is about 33% higher
(75/55)^2. That energy is only going to come from one place with no
power -- trading in altitude (potential energy) for kinetic energy.