From a dual passport holder let me tell you now that they will not let you through the land border if you stamp out on one passport and stamp in on the other. However, you can do this when flying. So, to Savanakhet, you are going to have to fly to Vientiane and take an internal flight/bus to Savanakhet
i.e. you shouldn't have to pay 1900b every time. That sounds wrong. The only cost with an F visa is the initial issuing of the visa if you don't have a diplomatic or official passport (which was the case for me).
I often found immigration officials confused my visa - having an F visa in a regular passport is quite rare, but entirely possible. I remember once arriving in Phuket from an international flight (where they have even less exposure to that) and it sparked an informal conference of about 12 immigration officials debating the legality of my visa.
btw, is your employment contract in order? That was the issue for me - when I was working as a short term consultant (still on an F visa) they were often cagey about extending....
Well, I was travelling all the time, so it was never an issue. However, you either border run or, as per your previous post, your admin staff should just extend you.