Fixed! Changed fuel pump and filter. I've tested it in hard mode with the gas fully opened, and it is working just fine.
I think the pump was half-dead. It was able to pump the fuel while cold, but when it gets overheated - just stops giving full pressure.

Thanks for all of your advices.

I've put different fuel pump inside. It is a Bosch pump (15$) that is used in lots of cars, and looks like same pump is sold as spare part for XT660. I had to remove fuel level sensor(useless) for now, to fit the new pump.