Just wanted to quickly update since I asked about applying for my 2nd SETV in Vientiane last week.
Everything went smooth and it was very easy. No need for the 3 proof ofs, as Tod said in my post. Crossed back into Thailand at Nong Khai with no issues. In fact, now that I think about it, I don't think anyone said anything to me at all. Oh no, that's not true. The Lao immigration officer did look at my US passport and saw I was born in Korea and was like "Oh! American AND Korean!" Then we talked for a minute about my mom being Korean and my dad white. We laughed and he asked me to wait at window 3. But otherwise it was handing things over, a quick glance from my passport to me, and then getting things handed back.
Oh! I also already had my applications printed and filled out and both Lao immigration and the Thai consulate took them.
Thanks to everyone who helped!
TLDR : Answer Summary
The user successfully applied for their second Single Entry Tourist Visa (SETV) in Vientiane without any issues. They reported that the process was smooth, and contrary to previous advice, there was no need for three proofs of documentation. Their experience at Lao immigration and the Thai consulate was positive, involving a brief conversation with an immigration officer about their background.