FYI, at one time, many years ago, I was tasked with a similar issue, and while I could never successfully guarantee that every pixel was "on snap", the application didn't require such accuracy.
What I did was to create a calibrated grid (as you have done) and exported it to a format and program that allowed me to vary the output size of the print. I was using a "C" size plotter at the time, and through trial and error found a print scale that gave me the one-to-one output that was needed.
Now today, there are a number of bitmap (raster) to line (vector) conversion programs around, and while many can give a rather nice DXF, the issue is still getting the scale correct. I have not used any of these programs, but I would think that a good DXF output could be manually scaled pretty easily into a CAD program to get the accuracy desired.
However, if you use "Save Image" (the camera icon in LDE), you will get the "Size JPG" screen. Keep both scale settings at 100%, and save as a file. Now go to "Image Control" and open this drawing. You now have a drawing that you can print, and using the printed grid, you can scale it.
But because I wanted to try it for myself, here's something even better.
Using a 12" grid, I created a cabinet shape I could scale for reference. (Corner openings are 12" square with 0.5 thick material all around. See attachment square0.gif). Taking this to the LDE, I found that by setting the grid in LDE to 1.47875", I was able to recreate the same "virtual" image, and note that it is (of course) still the same dimensions. (See square1.gif)
Attachment Square2.gif shows the printing options in Image Control, and with the laser printer that I have, this prints this page with the 8 grid "blocks" every 5 inches, which is 1.6 blocks per inch. If the actual grid blocks are 12 inches at full scale, and the blocks here are 0.625", than my print is scaled 19.2 to 1 (12/0.625) Thus, this print scale is then 0.625 inches = 1 foot. The figures may be different for your application, but the procedure should be the same.
MRK

- 150.5" square, on a 12" grid
- square0.gif (42.81 KiB) Viewed 5421 times

- Same shape and grid in LDE - 1.47875" grid
- square1.gif (41.78 KiB) Viewed 5421 times

- Printing options in Image Control.
- square2.gif (40.9 KiB) Viewed 5421 times