KMetalMind: Really thanks for all the info and ideas!
Tried DosBox SVN Daum and vsync is fixed! Had to change some settings, as overlay didn`t scale up for some reason...
Thanks KMetalMind, those settings fixed everything completely, I'm pleased to say! Thanks too to all the other patient people who helped along the way, leading to this - and other - improvements as well as solutions. It really seems like different setups were sort of working for different people, with few saying that any method solved everything without compromise. This one, however, fixed it 100%. Cheers!
*Edit*. I've just noticed the image is slightly squashed horizontally. If you look at the sun on the very first stage it looks squashed horizontally / stretched vertically / whichever way you want to look at it (it looks wrong).
To avoid a stretched or squashed image on a 16:9 display, you could use:
fullresolution=original
output=surface
aspect=true
If you then switch your display to 4:3 mode it should look right and the sun won't look like an egg :P (well, oval).
The only downside is that in 4:3 there will black borders all around and the whole image is smaller on-screen. I personally don't mind that too much because the tradeoff is a more natural picture (less blown up and pixelated), but that's a matter of personal taste.
note: 16:9 looks horrible when using output=surface of course, with a squashed-looking picture.