Two things to note on tone mapping for HDR games:
a) unlike movie which are mastered to a peak brightness which is generally limited to the peak brightness of the mastering monitor, and therefore does no use the full 10,000nit input range of ST2084, games are hard coded to use the full 10,000nit input range. This can mess up and confuse some tone mapping if it tries to render the entire 0-10,000nit range.
I use a Lumagen Pro, and set the clipping point to around 6,000nit input. In the absence of that you may need to implement a separate tone mapping curve.
b) Perhaps more conveniently for most users, most PS4 HDR games that I've played generally have a brightness slider in the video settings that allows adjustment of the HDR rendering to better suit the peak brightness of the display, so a suitably bright image should be achievable simply by adjusting that to taste.