Instead of returning from Laos with another visa exemption why not instead return with a multi-entry tourist visa obtained from the consulate at Savannakhet - assuming, of course, that you can meet their requirements (see link below)? That should give you more than sufficient headroom to stay in Thailand (with border runs every 60 days) until your child is born.
https://savannakhet.thaiembassy.org/th/publicservice/104412-tourist-visa?page=5d84a44c15e39c26b400453e&menu=5d84a44c15e39c26b4004540