Maybe simpler than you think. Pull drivers side wheel, look at side of tranny. Is it sitting on, or very close to the subframe? Bad mounts can cause this issue. Also, it may come & go, depending on how the mount resettles after jumping. Probable culprits are the transaxle mount (under airbox) & rear roll resistor (look up from bottom between firewall & tranny)
The drivetrain shifting may also account for strange steering response.
Andrew