Hello HDR57,
Before springing for a neck reset, I would recommend you consider the possibility of installing a Bridge Doctor. They're made to reduce the bellying that often occurs behind the bridge -- the effects of decades of string pull.
Your photograph may be misleading, but it appears to me that there is significant bellying behind the bridge of your guitar. You can tell how much by laying a straight-edge across the lower bouts, parallel to the bridge, and seeing how much of gap there is between the center of the top, where the bridge is, and the edges. It's not unusual to find 1/8" to 1/4" variance, meaning that your bridge may be riding that much higher than it should be.
The Bridge Doctor flattens the top, which lowers the bridge and eliminates any bridge tilt, which can improve intonation. It also anchors the bridge to the top of the guitar -- bellied tops often cause bridge-lift, which occurs because a flat surface (the bridge) won't adhere very well to a curved surface (the top of your guitar).
Can you slide a thin piece of paper under the back edges of the bridge?
You may also find that the Bridge Doctor improves the sound of your instrument, either because it allows the top to perform the way it was originally meant to, or because the the BD transfers sound energy directly from the bridge to the sides of the guitar, as the maker claims. Or both, I suppose.
BD's are cheap -- the basic model you can find for under 25 bucks, including shipping -- and they're relatively easy to put in. I've installed them on more than a dozen guitars over the years and have had positive results every time.
Always the top is flattened and works efficiently again. Sometimes that comes with no discernible change in sound, but sometimes there is a dramatic improvement in sound.
I usually have to make a new saddle for the guitar after the BD is installed, as once the top has been flattened and the bridge lowered the strings buzz because the old saddle is too low.
I've probably owned (or worked on) between 150 and 200 guitars over the years. All but two of them were used instruments, some going back to the '50s.
I've managed to get all my guitars working again without the need of a neck reset.
Good luck!
Glenn