Hi Martin Dušek,
Please test the FRDM-KL27 SDK code :
SDK_2.5.0_FRDM-KL27Z\boards\frdmkl27z\demo_apps\power_manager
1. modify power_manager.c, line 674 to:
ch ='G';
2. modify power_manager.c, line 266 to:
ch = 'S';//GETCHAR();
Then this is my FRDM-KL27 power consumption test result:

This board's chip is KL27Z64VLH4,1n87m mask, totally the same as you.
So, I highly recommend you test the official SDK code, just to check whether it is the software problem or the hardware problem.
Wish it helps you!
If you still have questions about it, please kindly let us know.
Have a great day,
Kerry
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