Just for a few data points. This has been a very long thread, so I might be repeating something already mentioned.
A reviewer on the Kaidomain site mentions exaggerated lumen ratings. No doubt these are very bright, but here's a link to the Cree XML-2 LEDs used in this lamp:
http://www.cree.com/led-components/products/xlamp-leds-discrete/xlamp-xm-l2
Cree rates each LED at around 500 lm (calculated; not measured) with a 2 amp drive current. The data sheet says max 3A drive current, but doesn't spec output at that level.
Forward voltage varies between 2.85V @ 700mA up to 3.3V @ 3A.
All the above numbers are per-device (3 devices in the product being discussed).
Based on Aluminum's recent post, it would appear that the product actually has in internal current-source driver for the LEDs, so we don't really know how much voltage is being applied to each LED. Does brightness seem to vary any if raised above the level that 'turns it on'? If not, there should be a 'sweet spot' of voltage fed into the product to minimize current and heat (the internal driver's most efficient operating point).
To the issue of local grounding: Most will probably get away with it; it almost always works with lights. But with switcher type power supplies, if the plane has, let's say less than ideal, grounding practices on the rest of the avionics, noise producers like old style strobes and newer stuff like switchers can push noise into other stuff via ground paths. There is lots of griping on this forum about LEDs causing noise in avionics, with little way of us knowing how the rest of the complainer's plane is wired. So an extra run of wire might not be a deal killer with that wig wag.
Charlie