I believe that the cause of what you are experiencing may be that the screws thread solidly into both the body and the neck. This is not a good recipe for a tight neck joint since any gap that exists when as the screw penetrates through the body and into the neck cannot be drawn tighter.
When you do this with all four screws you effectively have as many as three locked screws because each one may have slightly pushed the gap apart while it was threading into the neck and, as I said, effectively locking the previous screw in tighter.
One of the screws should still be loose enough to back out, so check each one carefully, and after that one is out there should be another that is a little more movable... and so on...
I think you can do it, just be patient and make sure you are using a screwdriver bit that is engaging the head solidly and push it in tightly while you are attempting to back it out to try to avoid stripping the head because if you do that then it's game over... then only destructive methods will be your option.
The moral of this story is that the body should be drilled to allow the screw to slip through without threading into the wood. Many manufacturers actually do not do this and can get away with it because apparently they have methods to clamp the neck and body together while it's screwed together. I sometimes notice this when I take apart a bass, like my Lakland 55-60 for instance. I reamed out those holes before I put it back together so I could pull the neck down nice and tight.