When you say the "vertical one, going into the frame", are you taking about the screw that goes through the top of the swingarm near the rear axle? The swingarm has a threaded insert pressed into it that is not supposed to move. Without seeing it, it sounds like the threaded insert is spinning; either that or the screw is stripped.
The screw can be a pain to get out if the insert is spinning, but one trick is to put side-force on the screw and try to jerk it in one fast motion to break it loose. It doesn't sound like there is enough room, but if you can get a punch, screwdriver, or small cold chisel under the chain guard, try to hit the top of the insert so that it dimples into the swingarm to lock it in place.
I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on the other. -Macbeth knew I.VII