Here's something you can try. You can enter Thailand, I think, as normal, by land.
TRY getting a single entry visa from the nearest Lao consulate. According to:
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"Issue visas for visitors who intended to visit the Lao PDR with non tourist purposes only. Visitors will have to submit requisite information on their health and related documents to the Lao diplomatic missions *in the country they are resident* for approval before the intended date of travel."
I DO NOT know what the bolded part means. If they do sell you a single entry visa, THEN get a medical certificate, and fly into Vientiane International. Once you're in Vientiane, cross back into Thailand via Friendship bridge.
That's the only option I can think of.