I think the problem is incompatibility of PNG format with exif and icc data. RT does not write/read the iic data when exporting/opening PNGs and auto applies sRGB primaries and gamma 2.2 at opening.
I would suggest using (compressed) tiffs when exporting … which are fully compatible with icc data.
For the existing PNGs you can apply as custom profile the profile which you used for exporting and then the rendering will be correct 