I am a sucker for new gear - hopefully not quite ‘all the gear no idea’!
I have previously looked at both the Dodotronics pieces of kit that you mention, to see whether they could be of use to me. The slight problem I have with both is that although I love kit, I am also a big fan of 32bit float recordings.
With the interface you can use your phone like a proper recorder (you can monitor on headphones) and also use Merlin (or other apps), but I recall that the interface output to the phone is max 24 bit non-float - in fact I am not sure whether any phones can handle 32 bit float files. So the interface saves having to buy a 24 bit recorder, you get a simple way to use Merlin, but you sacrifice the advantages of 32 bit float. The Merlin bit you can solve another way - if you have a line out on your recorder, you should be able to feed this to your phone (but this is more kit, cables and clutter than the interface option).
The compact dish is a bit different. The dish is the little brother of the HR dish, and I understand that it is a stereo parabola with integral Plug in Power mics. For me the beauty of the dish is the size, which could be a great advantage for travel (or even a long day in the field). But I would want to couple the dish with a 32bit float recorder, which would then mean I would need a device with a stereo mini-jack input. All the really small 32bit recorders are mono and the reasonably sized Zoom F3 recorder only has two XLR inputs, so would not be comparable without an additional adaptor. To have to carry a full sized recorder (I know they are not huge) or add an adapter, seems to me a bit against a compact and minimalist parabola set up.
The compact really has been developed for cameras, and whereas you can purchase the kit version with handle, I personally see this as a compromise - a small format parabola (perhaps for travel), but one that will not yield as good a results as a full sized parabola. For me the lack of compact 32 bit float recorder with stereo PiP inputs, means it is not perfect as a travel option.
Obviously gain is also proportional to the area of the dish, so a full sized dish will create more gain than the Dodotronics compact dish. So a big question is how close can you get to birds in Australia? If you are looking to record birds singing from the canopy of the rainforest in Darwin, then perhaps the full size parabola would be better? It you can get near enough, then I think the a the compact will likely outperform any shotgun option (at least for medium to high frequency calls).
I wouldn’t recommend the MKE600 for distant stuff. I use this mic as my holiday kit, attached to a Tentacle Track E recorder. It is a really compact set up and good for close birds, but I am sure that the mic high gain setting will create a lot more self noise than a parabola. Also this small shotgun will be much worse at rejecting off axis noise (and of course it is nicer to have stereo rather than mono).