LQ,
P035x DTCs are often caused by the coil connector or harness as well as the COP itself.
Pull the drivers side coil cover off, remove coil # 7, second from the back. Don't remove the plug, look down into the plug well and see if there is any water or oil down there. Do not remove the plug if there is.
Coil G also known as #7 is shorting to ground, you'll need to check coil and connector.
Myself I'd swap coil 7 to 6 and 6 to 7, clear code with OBDII reader and try again. If the problem moved to # 6, I would then realize it's the coil itself. If not then the problem is related to the connector or harness to #7
As with any used LS that show symptoms of running rough or such, I'd prefer to pull all coils, look down wells before removing plugs, if dry, remove plugs, throw it all in the garbage and replace all coils with Ford OEM DG529's. All new NGK Iridium plugs correctly gapped and verified at 0.040mm, even .038 and .039 is nice. Use dielectric grease inside the coil boots. Reseat all coil connectors gently and ensure you feel and hear the little click as it snaps in.
I'd even run it with the coil covers off for a bit to keep an eye on them until 100% sure problem corrected.
I wouldn't screw around with mismatch coils and plugs, it's either all new fresh OEM stuff or nothing at all. All at once, not one coil or two plugs here and there ... waste of time!
CARFAX states coils replaced two year ago means jack ... should see the crap I've pulled out from under coil covers. Shops and dealers tend to only replace what is broken, thus after a few visits, you end up with all mismatched differant aged coils and plugs. NOT GOOD.
Up to you of course, what do I know!
GLWR