EFI fails to boot Linux with GRUB - blinking cursor screen of death

I bought an HP Probook x360 11 G1 EE laptop with an EFI boot and Windows preinstalled. Since there's no option in the BIOS to support legacy boot, I can't do without EFI.

I tried EasyBCD to install Linux, but EasyBCD says that it cannot install Linux.

Next, I tried Grub2Win. But when "testing to boot" into GRUB, the system just hangs whilst booting with a black screen and a blinking cursor at the top left of the screen.

So I'm pretty sure that if I just let some live Linux USB modify the master boot record, Windows will not be able to boot anymore. I don't want to try that.

What can I do to boot Linux? What is this new kind of EFI boot that seems to be locked to Windows only?

Additional note:

In this comment roaima pointed me to a forum thread about a related issue with this laptop that suggests that the problem may arise from some incompatibility with this machine and GRUB.

As alternatives to GRUB, I've heard about Syslinux and rEFInd, but I've never used them. Does anyone know of an easy way to try them to boot Linux without risking breaking the working Windows boot?

Update

When I've finally found the options and ISO that got a live linux usb key to boot, Ubuntu install failed at the "grub2 install" stage. I think this confirms the fact that there indeed is some incompatibility between grub and this precise laptop.

Answer

I tried EasyBCD to install Linux, but EasyBCD says that it cannot install Linux.

Considering yours is UEFI then it's totally expected. EasyBCD does not work in UEFI. EasyUEFI is a similar tool but for modern systems. Usually you don't need any special tool for dual-booting. Dual-booting Windows+Linux is easy and well documented.

Unfortunately there are exceptions: Some notebooks don't have the correct UEFI specifications and tend to boot by name instead of EFI entries (and the name they boot is always "Windows"). Even so, if you followed the above instructions correctly you should always be able to select "Ubuntu" at boot time in the firmware (UEFI) settings. That's when third party software like EasyUEFI may come in handy.