Boot-Repair seems to succeed but still boot into Windows 10

I applied some Windows 10 updates last week (I only use the Windows partition when necessary). Today I discovered the laptop would only boot directly to Windows.

1. I ran boot-repair and it asked me to disable SecureBoot and try again;
2. I disabled SecureBoot and ran boot-repair again - no success;
3. I tried the Boot Repair disk instead of the Live CD - no success
4. I ran "bcdedit /set {bootmgr} path EFIubuntushimx64.efi" as suggested and confirmed the setting with Visual BCDEdit - same result: system boots directly into Windows

Both Windows and Linux were installed using EFI and have been working.

Everything seems to have succeeded but without any change. My boot info summary is here: http://paste.ubuntu.com/20878949/

(And yes, this is Linux Mint, not stock Ubuntu, but the forums here seem much more active and as I use this for work, I need to find a solution).

Any assistance is appreciated. I've looked through the summary but nothing obvious jumps out...

Thanks!