I have been using a measured HRFT (measured on Brüel & Kjær HATS (Head-and-Torso-Simulator)) to create binaural sound from mono recordings. As the HRTF's were recorded with the sound source relatively close to the HATS it also generates sound that I personally perceive as being close to my head. (even if mono recording was carried out with a major sound source being far away). Is it possible to make the resulting binaural sound appear as being further away by some "simple" way? (perhaps it is just an effect of my particular hrtf compared to the hrtf of the HATS)
To the best of my knowledge, most HRTFs that are meant to be distributed are recorded in an anechoic chamber. Additionally, most of them are recorded with the sound source being reasonably (I know this is not a very specific term, but to my knowledge there's not standard for the procedure as of yet) large distance, so the resulting sound field can be considered to be planar (plane wave approximation). This means that in this case, the ILDs will depend only on the geometry of the head (as well as the torso and pinnae) mostly due to shadowing effects (there's some "amplification"/constructive interference on some frequencies where the diffraction can cause a delay of an integer multiple of a full wavelength for some angles) and the ILDs will depend only on the angle of incidence.
In this way, the effect of distance is eliminated. Of course, this is just an approximation and the intuition is that you should go as far from the source as possible in order to minimize the curvature of the resulting wavefront. If the curvature of the wavefront is not small (I apologize for not being able to provide quantification on this topic) then some extra attenuation will be introduced due to the inverse square law (if the distance between the "head" and the source is somewhat long, this attenuation term can effectively be neglected. This is equivalent to minimizing the curvature). Additionally, some complexity will be introduced to the diffracted components adding extra complexity to the resulting HRTFs.
From the information you provide, it seems that the HRTFs you are using have been recorded with the distance between the source and the "head" being quite short. To my knowledge there's no "proper" way to get rid of this. Trying to "repair" the HRTFs is not something that can be done..., at least not manually. The resulting transfer functions are way to complex to be able to change some parameter (like the relative amplitude) and provide the desired results. Of course, I may be wrong on this one.
One more thing to note is that you should try to equalize your headphones to get rid of their transfer function. On top of that, you should make sure that the only part of your ear's transfer function that remains in the final transfer function is from the point of the recorded signal (on the "head") and onward (towards the middle ear).
Finally, you should keep in mind that most (if not all) of the time, the resulting audio product (after convolving the mono file with the appropriate HRTFs) is perceived as being "inside your head". This is due to the fact that there's often some degree of correlation between the two signals and the fact that micromovement of the head does NOT alter the perceived angle of incidence. This kind of sounds are perceived to originate from within your head just because the real-world sounds that have such characteristics do indeed reside somewhere "inside your head".
A very good example of that is chewing. Due to the fact that the relative position of your mouth to the ears is constant no matter how your head is oriented, the localization of the chewing sounds will be constant. So, if the movement of your head does not change the perceived location of the sound (you should use a gyroscope or some other mechanism such as accelerometers to pick up head movement and change the HRTFs to be used), this sound is perceived as being somewhere "inside your head". You should be aware of this effect and make sure that you do not attribute your issue to it.