I set off on this same quest at around 7:00 AM this morning. Like you, I found Virtbs' Land's of The Lore "Dosbox Direct3D HQ6x" shader. Googling for an HQ6x shader brought me to this thread.

I have the same config as you, using the following values:

   fullscreen=true
   fullresolution=1920x1080
   output=direct3d
   pixelshader=HQ2x.fx
   aspect=true
   scaler=hardware3x  

I'm using Gulikoza's dosboxcvs-090704 with DaggerfallSetup. (DOSBox 0.74).

I play all my old games on my M11x output to a 22" display in 1080p (Unless mobile of course). Your GeForce GTX 970 should run circles around my GeForce GT 540M/i7-2617M. I'm getting excellent performance.

I can't find any evidence of an actual HQ6x shader and Virtbs seems to have refused multiple comments in his 3 videos asking him where to find the shader.

The best I could find was this:

http://www.hiend3d.com/hq4x.html

But with no download link.

I also found the following comment from gulikoza:

Pixelshader is activated when dosbox requests hardware scaling. Hardware scaling can be setup either with hardware scaler (hardware2x or hardware3x) or with window/fullresolution options. If for instance you set pixelshader=hq2x.fx, scaler=none, fullresolution=1920x1200...then hq2x will be used to scale game resolution (eg. 320x200) to 1920x1200 when in fullscreen (the scaled resolution will actually be 1600x1200 if aspect=true is also used, so the scaling will be x5 horizontally and x6 vertically).

So, based on this comment, perhaps Virtbs was being misleading with the title of his video?

Finally, I found the following:

Comparison to hqx, which is very cool but these shaders appear to be compatible with NES emulators such as Nestopia, rather than DOSBox. (But something for me to keep in mind for other games, like Dragon's Quest, a childhood favorite of my wife.)