I was told years ago from my Thai bank that any value over 10,000 USD is liable to a higher risk of investigation for money laundering, meaning legit transactions could be delayed, I’m not suggesting your payment has been delayed nor am I suggesting any illegality going on here but if you’ve made regular transfers above the 10k usd then maybe they’ve been monitoring your transactions and thus caused issues.
Usually they check, but I’ve been asked once when using a one way ticket if I’d planned on doing an extension once there, (which I did ) this following the check in desk checking through my passport pages and I guess them seeing mostly yearly extensions or yearly multi entry visas with plenty in out stamps, so you may get away with it but best have a dummy onward ticket just to be sure.
Even with the paperwork I’d still leave the car at the border parking, savannakhet its easy to find a Tuktuk anywhere, you may have to stay at least overnight, but you can ask the immigration when you check out whether they will allow you to return early evening, be aware of fake booze, I brought back a bottle of gin from the nice duty free shop in town a couple years back for a friend, I was quite surprised that he finished up binning the bottle after pouring a glass.