How can I travel to Laos or Cambodia with a single-entry Thai E-visa?

Just time your visit to the other country towards the end of your visa, then when you come back into Thailand you'll get a visa exempt stamp good for another 45 days, with no trouble at all. You don't need a re-entry permit. If those 45 days aren't enough, you can get a 30 day extension onto the end of those 45 days for bt1900 at immigration. Don't worry about your tourist visa. Just spend the beginning of your vacation in Thailand, then to the other country in the last month. Angkor Watt in Cambodia, or LuangPraBang, and VangVien in Laos are very nice. You want a lifetime memory, go to LuangPraBang in Laos, then rent a private car, or van, and go across the mountains to Phonsavan and the Plain of Jars. If you don't spend the extra money for a private car, then you are jam packed in a van, and have no choices at all about where you stop for the five hour trip. The trip over the mountains, and it's a very good road, gets pretty rural, then the Plain of Jars is ancient history, of 3000-4000 years ago. Then fly back to Bangkok, or take the night bus to Vientiane and cross back into Thailand in the morning, or stop along the way for a few days in VangVien.

In theory you could get a re-entry permit on a tourist visa. Not seen reports of anyone that has, but it may be office dependent.