Before removing the rear indicators again, just try plugging in the led ones (plus resistors of course!) into the loom (they are earthed through the wires rather than the frame so don't actually have to be mounted to work). That way, if they still won't work with the engine running, you won't have to remount the originals (again!).
I got caught out like this when I fitted mine
http://www.ukmonster.co.uk/monster/s...52&postcount=2
But, in our defence, there's nothing in the installation instructions mentioning this is there?