However, this doesn't answer your question completely, since hp might provide even more current firmware-versions.
On my system the firmware version is the same as yours, 4PC10365, the only difference being: I already DID install the firmware upgrade!
There is another problem with the firmware upgrade 1.20 from the hp-downloads-site:
Installing this upgrade is working fine until necessary reboot: Reboot fails every time, producing an error 0x0000098 "application missing or corrupt", when the file loadvf.bin from the upgrade-directory should be booted.
I am worried that the firmware-upgrade might not be complete.
Intel-Tools all state that the firmware is fine and current, perhaps because they check for the older Intel-Version.
My Install of Windows X64 Pro is an EFI-Install. Might that cause the problem?