, Maybe OP has to consider, as it depends on what actually "my wife does not qualify for her own O-A visa" part means. In most requirements same to Non-O retirement visa
You can apply for Non-O based on being a spouse to a Thai national (Spouse and Family Visa) or Non-O retirement. Both are single entry visas valid for 90 days and give you 90 days on entry. Then you can apply for 60 days family visit extension at the local immigration office. No border run for 4-5 months.
Do you mean Non-OA visa for retirement? That visa requires you to have specific insurance to apply. But other Non-O single entry visas don't require insurance.
BTW, You have a good and understanding employer who makes the paperwork as of the last day of your current stamp so that you are not overstaying even after you finish working with them. Usually, a termination letter is dated as of the last day of your work.
Your employer is basically right. You are the one who is responsible for an extension stamp on your passport. They can support you, but they cannot cancel your extension without you.
Go to cancel your work permit and extension to leave Thailand without issue. You need to check with your local immigration office and labour office to see which is the first to be cancelled. Those procedures could vary depending on the province.