Hi Pawel,
Before we do any deep discussion on the different possiblities I would like you to run the same test with an out-of-the box eval kit from TI. Any chance you can remove all the modification you have done? The TI eval kit has the best performance possible to achieve with the CC85xx, and it would be interesting/necessary to see if this is also struggling in your test environment. The last thing we want to do is start chasing a ghost...
Best regards
Kristoffer