AD9363 is a derivative product of AD9361 and should behave the same over supply, temperature and lot to lot variation as AD9361.
I think that the issue you are seeing is due to software and/or hardware on your platform. Since you have convinced yourself that AD9361 on ADI's evaluation platform passes your testing I would recommend placing it in your hardware platform and seeing if it passes your testing. I suspect that you will find AD9361 having the same issue as AD9363 in your hardware. The two parts are pin and software compatible.
If you find the cost differential between the two negligible in your case, you can migrate over to AD9361.