I'd run with what you have and take the scale length as 624mm.

If you put that in the StuMac calculator, then you get this:

Click image for larger version.  Name: 614mm scale length.jpg  Views: 184  Size: 96.2 KB  ID: 37094

If you look at your photo with the 12th fret and ruler, then the 10th fret position looks to match up with the calculated 273.8mm (though you could really do with a better ruler with individual, and thinner lined, mm markings, for this type of work.

You can measure a few other frets to confirm, but if they match, then I'd run with 624mm as the scale length and position the neck accordingly.