with a typical 15km surveyed obstacle clear area
First, the AFM charts give the operations engineers (or the pilot) the data to do the sums and match performance capability (actually certification or net performance so you have a bit up your sleeve) to the runway environs. The AFM data is vetted fairly heavily by the Regulatory Authority (FAA etc) so it is likely that that data is reasonably OK.
When it comes to applying the AFM data to the real world, there are all sorts of folk out there doing the work - some well, some not quite so well, and some quite dreadfully. I guess you are with one of the QF entities (?) so, presumably, QF ops eng looks after your performance - in which case it probably is done with a reasonable degree of rigour.
are my RTOW charts ensuring .. that I'll reach final takeoff speed/config (to commence the 4th segment) by the end of the 15km?
I can't offer any comment on that question without having a bunch of data to do some check analyses myself. The question needs to be addressed to your company operations engineers. If they tell you that the net takeoff flight path analysis doesn't take care of you right up to LSA/MSA .. then I'd be having a talk with the union for starters ... albeit the pilot unions in Australia have been somewhat on the back foot for quite some time now ..
I can't recall doing any ops eng work with -300 so I can only speak generally. Fortunately for turboprops, the third segment is comparatively short so the problems further out (usually) are somewhat less than might apply to, say, the twin jets. As I recall, the DC9, for instance, with a significant speed delta between V2 and final climb speed took forever to get through the net third segment - not hard to see upwards of 50nm OEI to get to 1500ft. I never did incline to the airlines which figured that it was a pilot problem to worry about post 50,000 ft (or 15km, if you prefer) in the Type A chart ...