I had just composed a lengthy reply but hit reply rather than Post and lost all the information:
A lot of variables to consider when you go to do this:
Here is the essense of what I wrote:
Your camera weighs about 600g (I wouldn't recommend building your own gimbal at this point):
A gimbal (photohigher AV 130 or one upgraded MKTR) is another 500g (I would go with Photohigher - it is upgradeable to 360 pan) - we use MKTR and it works okay but took some tweaking.
The camera you are trying to lift looks like a quality setup so I would recommend an octo or Hexa configuration. Octo would be my suggestion since it will provide the best redundancy in the case you lose an ESC or motor mid flight.
That margin of safety and redundancy comes at a cost to the wallet as well as to weight.
I can cut to the chase here and make a recommendation on what you will need for motors and props because our current setup lifts a similar sized camera.
The total weight of our octo setup is just over 5Kg (including everything: frame, camera, gimbal, 2 - 4s 6000 mah batteries in parallel, video transmitter, motors, ESCs, etc.)
Our cheap DIY wood frame is 914 mm motor to motor. The frame sizes you suggest are probably too small for your camera (I tried starting out with exactly that 550 frame in an X8 arrangement) and there was just not enough room for electronics and props - no point of reproducing my mistake. 914 mm is a nice size for an octo with 12x3.8 APS props.
We also used Avroto 2814-11 motors (100 g each). Fight times 6-7 minutes (I am conservative with draining batteries).
Start playing with number in
eCalc - I don't totally trust it but it will get you into the ball park.
Hope that helps and there are lots of build threads by folks who have done similar builds to what you are attempting, check those out and you will get a sense for ball park specs that you will need to look at.
Oh, you might be able to cut corners by reducing the frame size slightly and going with 11 inch props and further reductions by going with a hexa configuration but I have chosen not to go that route.