If it's not too late, some comments:
Sorry I don't have the mini XLR adaptor leads for the BMVA 4K or I would try it out for you.
On the plus side, the Rode NTG2 will work from an internal AA battery, but as stated, it is much less sensitive than the ME66 and will need the gain cranked up quite a bit more.
Also, since you have mentioned using the mic outside, the Rode will definitely need gaffer tape or PVC tape over the HPF switch and the XLR connector if there is any wind. A Rycote softie will stop wind noise from the front, but its the rear end that's the problem. Or you could stick the thing in a Zepplin.
The Videomic Pro (mono ) has a similar problem – not sure about the stereo version.
Do you need to record in stereo? ME66 or the Rode will give you one channel of audio, you could fix that in post with your NLE or find a splitter (preferrably active) to send to both channels on the BMVA 4K. A splitter cable probably won't cut it, even with the ME66.