PR is a permit to stay indefinitely. You need a non-quota immigrant visa and re-entry permit if you want to leave the country.
Think of it this way -----> Once you obtained PR, you are no longer "on the clock" while in Thailand (you never need to leave). However, when you leave Thailand, the non-quota immigrant visa and re-entry permit start a 365 day timer and you need to return before that one year period or lose your PR.
If you're not listed on a household registration, you're violating the terms of agreement for PR. The house registration is a direct link to the district police station that is charged with oversight of your residency in Thailand (Red Book). If you want to leave the country, and come back at least once per year, you need to sort out a sustainable long term solution for household registration.