In no particular order.
You cannot obtain a non O based on marriage if just engaged.
Until you are married you could go the non O based on retirement.
You could wait till you are married and use some gap stop method in meantime such as visa exempt entry (might be 60 days soon) + 30 day extension..
You only have 2 weeks remaining on your stamp.
How did you enter Thailand. Visa exempt 30 day stamp? If so you could obtain a 30 day extension.
Forget ED visa etc.
You do not have to adopt and of her children.
You state....."Youngest kid becomes your responsibility too when married, don't have to take any action"
Perhaps poor expression. Her children and your wife (future) is your responsibility.
Here is a thread outlining how to enter Thailand visa exempt and process to non O marriage and subsequent 12 month extension
In my post I have links to other threads. Read them all.