I have been doing some digging around this area and have come to the conclusion that while the traditional performance formulae (which can be found all over the internet) work well for a glider, they break down as soon as an engine is present! This is because engine and prop efficiency are not constant over power output.
I think the way to determine the best endurance speed is to set up the engine peak or lean of peak, and bring back the power until the plane just holds the altitude. But not so far as to allow it to fall onto the back of the curve.
Obviously the figure will vary with altitude, temperature, loading.
However, one may have a problem with engine cooling, so may have to run the engine rich, say 100F ROP, to get a cooler combustion.
Best-endurance speed might be handy for an extreme holding situation but is useless for normal flying - largely due to poor engine cooling. For my plane (TB20) the handbook gives a power setting which gives about 100-110kt - way more than Vbg for the airframe which is ~ 95kt.