I feel the need to put my 2c here too, mainly because I've been there as well! I started bird photography with the same lens (Sigma 70-300mm APO DG) and I came to realise a few things. Firstly, the lens itself needs to be stepped down quite a bit to get the sharp results I was after, but in order to do that you need quite a bit of light to get the exposure you need. Secondly, I came to appreciate the merits of a good sturdy tripod, a remote shutter release, and most importantly, good long lens technique. Thirdly, as it was previously mentioned, you need to get closer to your subject, and at 300mm you need to get really close to get the results you are after, which means you need a lot of patience. Unfortunately, birds aren't the most obedient models and, besides the occasional tame robin, they will flee as soon as they see you approach. So, just walking about with your camera in hand, looking for birds is a bit like shooting in the dark. You might get lucky but in most occasions you will go home with a few distant shots.
As for the 2x TC, as others mentioned, keep it for when you upgrade to a better lens. After my 70-300mm f/4.5-5.6 I bought a Sigma 120-300mm f/2.8 which was a completely different beast, very sharp, great colours and contrast, but still struggling with a 2x TC, so I ended up selling it and opting for a 1.4x instead. And we are talking about a £1700 lens. I can only imagine the results you are getting with the 70-300 and the 2x.
So, my suggestion would be to follow all the advice you got from this thread regarding your settings, forget the TC for now, and concentrate on getting yourself closest to your subjects instead of trying to bring them closer with zoom. You can never have enough focal length when birding, you must always remember that
. So, if you have a back yard, set up some bird feeders in front of a back window or a back door and wait. Or, like myself, if you don't have this luxury, try visiting a nature reserve with bird hides, or get down and dirty and conceal yourself and lie still for a few hours
And here are a few examples when I couldn't get a hide set up.
Lying on the ground with a blanket over me and a beanbag under the lens.
My one and only (crappy) KF photo, sitting still in some long reeds for a couple of hours, aiming at that particular perch. The only photo I managed to get of him, and it is a considerable crop, but still a photo of a KF.
Not a bird photo, but I was stalking this one for almost 2 hours before I managed to get close
And this one taken from my favourite and most convenient hide of all time...my car! Use your car, you'll see that you can get really close without disturbing them.
Sometimes you must use bribery to get them to comply. This one noticed I had some mealworms and came to investigate. You'll find robins are the first obedient subject you'll photograph, and you'll be surprised that wherever you'll find them they will get quite tame really fast if you have something to offer (anglers using maggots will know what I'm talking about).
Bottom line is, try to be patient and always remember that you'll need to get close to a very timid subject. And if you get your technique and approach down, you'll start to get good results in no time.
George