Hi Torquil,
What brand model etc.? Are you sure that there is no truss? Some Acoustics have the adjusting nut inside the guitar body and do not have an external cover on the headstock which can be misleading.
The saddle is lifting, which could be an indicator of improper humidity while in storage, or also a sign of loose or cracked bracing under the saddle. Both of those conditions can be repaired by an experienced Luthier if the instrument is worth saving. Most will gladly give you an estimate of the repairs free, so it is always worth inquiring. After any repairs have been assessed and completed the bridge can be adjusted to restore lower string/fret clearance.
You might be able to invest a couple hundred bucks and wind up with a highly playable guitar for just running it around for some "expert" opinions.
Good Luck & Take Care;
Doug
"what is this quintessence of dust?" - Shakespeare