Our fuel injectors are just forward of the cylinders intake valve. For gas to reach the EGR it would need to back flow to the EGR at the rear of the engine where the EGR tube attaches to the intake. i can't see how gas could get to the EGR from the exhaust side. Definitely check all your injectors.

Raw gas at the EVAP solenoid comes from the charcoal canister at the rear of the car and usually caused by a bad shut off valve on the canister.