Depth of field is a function of the ... and the desired diameter of the circle of confusion.
And the circle of confusion diameter is not an arbitrary choice: to get the sharpest possible image of an object, as you seem to want, the object should be within the DOF range computed by using a CoC value comparable to the size of the smallest feature that the camera (sensor and lens) can resolve. This means that you probably want it very roughly
the same as the pixel size; maybe more like twice the pixel size in practice.
To get beyond this hand-waving vagueness, experiment, or find an experiment that someone else has posted on the web! Norm Koren's site http://www.normankoren.com/
is often great for this sort of technical and experimantal stuff.
An easy, crude initial experiment is to make a sequence of photographs of a scene in highest quality JPEG mode, gradually opening up the aperture, and look at the file sizes. As OOF blurring increases, the file sizes get dramatically smaller, since the JPEG compression is smart enough to realise that there is far less detail in many parts of the image, and so compresses those parts a lot more. Check against how the image looks, and see how file size is related to perceived sharpness.
Indeed, some digital cameras have a "best shot" mode that chooses the sharpest of a sequence of shots on the basis of having the biggest JPEG file size.
A cautionary example of what would be a very poor choice of circle of confusion value for your purposes, even though some sources might seem to suggest it:
If you were to use a traditional DOF scale for 35mm format, which assumes a 35 micron CoC, with a camera like you F717 whose sensor has 3.4 micron pixels and which can resolve details as small as about 5 microns or less, that DOF scale would be counting some objects as being "in focus" even though they are blurred down to about one tenth the sharpness of objects at the focal plane; the image of each point at the supposed limits of DOF would be smeared into a circle of confusion covering about 100 pixels!
If instead you count something as being in focus only when it looks about as sharp as the sharpest part of the image, an appropriate value for the circle of confusion should be very roughly the same as the resolution scale of the camera, which with a good camera (including a good lens) is usually about 1.5 times the pixel spacing, because of the way that Bayer interpolation works. Teleconverters can noticably reduce sharpness though, as you seem to have observed.
P. S. Some things you can read in forums and even in photography books are written in the traditional context of film photography, and sometimes even specifically for 35mm format film and lenses. For example, they might assume the resolution capabilities and enlargment factors typical with such equipment. Even worse, they sometimes assume the more severe resolution and enlargment limitations of the films and lenses that existed half a century ago, when the DOF scales for 35mm lenses were standardized.
Some people make the mistake of taking these statements out of context, believing them to be universal truths, applicable even to cameras and lenses of far greater resolution and far smaller formats that are typically used with far greater enlargement factors.