I have been running HF mobile for over 30 years and have not found that a separate ground was necessary. The most important ground is at the antenna, especially on 40 meters and below. Here it is important to have a low inductance ground, that means as short and wide as you can make it.
My current HF mobile setup is is mounted on a plastic toolbox and wired into the truck main power buss with 2-12ga wires each, on the positive and negative. Battery charger clips go to the mounting posts inside the dash. It is secured on the passenger seat with the seat belt.
Left top down:
Rat-Shack SWR-Watt meter.
LDG AT-11 Autotuner
Uniden HR-2600
Right top down:
Amcom Clear Speech speaker
External speaker for the 2600
LED headlamp for putting on chains in the dark
Excess power wire that powers the entire box
ICOM 706MkIIg
Right top down:
External speaker for VHF/UHF
VHF/UHF Antenna diplexer
Kitchen timer for taking naps
Kenwood TM-733
Yellow toolbox under radios and Truck computer screen in foreground.
I talk the world with this setup, every day and put it in and take it out of the truck, every day.
Rich