This looks like a hardtail Strat bridge; definitely not the "Tune-O-Matic" of a Gibson. I've had intonation issues before that seemingly defied a solution. Here are some suggestions:
- First, what's the difference in tuning between the 12th fret harmonic and the 12th fret itself? You need to make sure the problem really is in the saddle length. Pluck the harmonic, tune that, then fret the 12th fret and pluck again. They should be exactly the same note. Equivalently, when plucking the 12th fret harmonic, the most lively harmonic should come with your finger touching the string right over the 12th fret, not in front of or behind it. This is less accurate, as the string will settle quite naturally and quickly into its harmonic standing wave.
- What's your neck relief? Put a capo on the first fret, press down the last fret, then slip a gap feeler under the string at the 9th fret (which is usually where the neck straightens regardless of the amount of relief). Fender recommends about a .010" gap (you can check this pretty easily with a cutting from your last E string; it'll be between .009" and .011" depending on preferred gauge which will be close enough); you adjust this gap using the truss rod. Some guys like their necks arrow-straight, but fail to realize that this increases the speaking length of notes between the first and fifth frets, lowering their pitch even when the spring is properly tuned and the saddles intonated. It's minor, but all of these adjustments are minor (so much so that you cannot do a setup by sight or feel).
- What's your string height? Depress the string at the 9th fret (to take relief out of the equation) and measure the height from the top of the last fret to the bottom string with a depth gauge. Fender recommends 4/64" to 5/64". Most guitarists I know like it lower than the recommendation, assuming they have a good neck; however, the problem with this is that it will lower the tension placed on a fretted string; great news for your fretting speed (and your calluses) but bad news if you're out of room.
- What's your string gauge? If you recently increased your gauge, say from 10-46 to 11-52, then even if the neck is adjusted to compensate, the string will bend less when you fret it, and that equals flatter notes, because you're not "pinching" the fretted notes sharp (in this case quite literally, Yngwie Malmstein style).
I typically have much more trouble with Gibson's Tune-O-Matics than with the Fender bridges; I end up with the notes trending sharp across all strings in the first octave because I like the action high which increases the tension of fretted notes, and the reduced adjustable range of the Gibson-style bridge saddles pretty much requires that you set it up their way.
If the saddle length screw is at its maximum and you really do need to go with a shorter speaking length, there's nothing for it but to look for a longer screw. Sometimes other saddles will have longer screws because the manufacturer expected to you have to bring those up more than you actually have to; if you have another, longer screw with plenty of slack, try switching. Check the parts and repair counter of your local store (and if you know of a good Mom & Pop repair shop in the area, make friends and see if they have something in the spare parts bin that they'll swap you for your current saddle screw).
The other thing you can do if all strings are at or near their minimum speaking length (maximum extension on the saddle screws) is to have the bridge repositioned; the luthier will remove the bridge, fill in the holes, then very carefully drill new ones an eighth of an inch or so further up and remount the bridge. This will give the extra adjustment room you need. However, this is brain surgery for luthiers; one mistake in redrilling the bridge mounting holes and your prize axe is garbage.
