It is 400k for 2 months in Chaengwattana for thai child. But they might flexible depending on their analysis of your statements. Some say there is no seasoning but there is. If you fall short of 2 months be sure to have way more than 400k. Also, they require pics inside the house, in front of door with address number and in front of your home or condo. Letter from school and pics in front of school with mother.
As for pushing back the date, not possible. Only options are indeed the 60 day visit family, if you haven't used it yet or leaving and getting back in with 60 day stamp and applying for a 3 month O based on thai child (400k no seasoning) not later that 21 days before your 60day stamp ends. Then extend 1 year.
From personal experience in Bangkok (Chaengwattana), they require all the above (pics at school with both parents and school name) and at home (with address, room number, etc.) as well as your child and mother at immigration. Birth certificate and housebook. No ID.
Biff Jones I flew in and out without exceeding 90 days... I am doing them when I stay 90 consecutive days in Thailand but not when I leave the country before the 90 day limit... then the count starts over right? Thanks.