Marry an Cambodian girl

I'm afraid you won't get away with it. Although it is stated that you should not have committed crimes in Cambodia I think when the criminal record shows up that's the end of the application.

You can choose for the quick marriage: arrange clothes for all, including parents, witnesses, get a photo session, go to a pagoda (temple), find a monk who is willing to do a short marriage ceremony and that's it. As you have photos of the ceremony with family, monk and so you can try to legalize the marriage at the local community office where the bride lives/comes from.

You can also just do a village ceremony, 3 days with tents, music and lots of booze, but you can't really register that marriage. It needs to be said that many marriages are not more than that: a village ceremony.

As Joe said, most likely you will only be able to have the ceremony - but be prepared to be shaken down by the local chiefs and/or police.

If it's important for you to be legally married, you should be able to get that done in Thailand easily enough. It won't be legally binding in Cambodia, but it should be almost everywhere else.