Just a note of clarification, 1200b for a single entry permit. I think it's 3800b for multi, but I may be wrong on that as I haven't done multi at the airport for years
Right generally speaking it's fairly quick and easy at BKK. The re-entry stamp office is after security, before immigration (but in the same room as immigration). If your flight is at 6, you're probably just before the morning rush (7-9am at BKK) so I would say you won't have too much of a problem. I still suggest you check in early (say 2 and a half hours before). The cost at BKK is 1200b. If it's quick and easy, then treat yourself a coffee and some breakfast!
If you need to go to Vientiane (notwithstanding the comment above), it's much cheaper to fly to Udon Thani, and hop across the border from there. You also need to remember that you apply at the Thai Consulate in Vientiane, not the Embassy. I would advise you stay somewhere near the river and get a tuk-tuk (or even rent a bicycle) to go to the Consulate, as that area is a bit of a dead zone at night and you won't find anything to eat/drink/do. It takes 2 days, i.e. you apply in the morning of day 1, get your passport back afternoon of day 2. If you fly via Udon, you can take a 6am flight up there, and make it in time to apply, and get a
****
pm flight back meaning only 1 night is necessary. Try to avoid applying on Mondays as it tends to be very busy and the wait times are quite long