To follow up, should you proceed with getting an exemption of stay stamp for 60 days, I would prepare the exact requirements related to that method of entry. Although this sounds obvious, in the past the requirements were not really enforced. I think to cover yourself, I would make sure I tick all of the boxes. I.e. ticket to leave Thailand within 60 days, live access to the required funds as per the requirement etc.
1. No. You canβt stay past the date on your extension of stay. Re-entry permit just maintains validity of your current extension of stay.
2. Yes more than likely, I would prepare to be thoroughly questioned when re-entering when doing this. The IO officer may show an interest in your plans. As you mentioned you will lose your extension of stay based on marriage and will have to reapply should you want to use a marriage based visa again.
you are correct about it being the landlords responsibility (as per the law) but they very rarely (if ever) get fined or even checked. In practice, the responsibility falls with the tenant as they are the one requesting a service from immigration and therefore must ensure the TM30 is up to date to facilitate the processing of their request. The tenant is also the one who usually pays the fine as they are the ones having to face immigration.