That radar track and R/T transcript is very interesting, but could have been a lot better if combined with the BOM Wx radar images of the same time interval.
Whatever weather the two pilots actually saw on departure from DN, it wouldn't have looked any better by trying to climb over it. NT and tropic weather is mostly cumuliform which means you can fly around it or around the rain falling out of it, and in fact outmaneuver it since you are 10 times faster than the weather in a C210. Visibility is a lot better looking under it along track than trying to climb to 10,000' then trying to weave along between the +15,000' tops that blind your actual view along track.
That is really the basics of flying in the Top End during Build Up or the Wet, and I can't understand how these guys were not trained in that or put it into practise. I've flown this exact same planned route a lot (a lot), and never once would I have considered tracking NW to enable a climb of any kind, if all I had to do was head east at 1500' and avoid the black scungey stuff.