v2.4 pg 40, Double Strike
I realize you're somewhat locked-in on the page layout because you already purchased the art. I'm going to pretend you can do anything you want. Maybe some of this gets bumped into "next edition" territory, but maybe you can squeak it in because it's split across multiple pages.
pg 39 - Basic Actions
Make a single attack with one weapon. An attack with an off-hand weapon has disadvantage unless you have the Ambidextrous talent. You may only take one Attack Action per turn.
Make a defense roll against one attack or counter one magical attack or other effect. If you have a weapon or small shield in your off-hand and do not attack with it this turn, parry with it to gain advantage on your defense roll. You may only take one Defend Action per turn.
pg 40 - Double Strike
As a Standard Action, make two attacks against an opponent with a lower initiative rank. Both attacks have Disadvantage. This counts as your one Attack action for the turn.
Wielding two weapons, attack once with each. The weapons must be light melee, pistol calibers 9mm or less, any laser pistols, or other energy pistols Damage d6 or less. Alternatively, fire twice at the same target using one semi-automatic (SA) firearm.
This bit needs to go somewhere else entirely, it doesn't belong here. Maybe the equipment section or the weapons list?
"Shields inflict Damage d4." "Improvised weapons inflict Damage dX."
Actually this is better. You should be able to parry with your main hand weapon too, right?
Make a defense roll against one attack or counter one magical attack or other effect. If you do not attack with it this turn, you may parry with a melee weapon or small shield to gain advantage on your defense roll. You may only take one Defend Action per turn.
I appreciate your feedback, but - as you stated - the layout of the Core Rules is now fixed and cannot be changed.
To answer your question: No, you cannot off-hand parry with your main weapon. Off-hand parry represents having an "extra" weapon that has not been used to attack allowing for its defensive use. It also adds an additional fighting style or option to the game. If the character were armed with two weapons and chose to attack with their off-hand weapon, then they would benefit from off-hand parry with their "main" weapon as they would have effectively switched the roles of their weapons.
Scribe of the Adventure System