Coming back with info with the possible software fix of the circle problem. Thanks to grob for helping me with this.
So you'll need adrian's fork (version) of the Marlin firmware. The M98 and M99 were never added to the official firmware.
https://github.com/ozadr1an/Solidoodle-Marlin_v1
use M98 to get current values and "M99 Xmm Ymm Zmm Emm" to set the values.
I can't confirm this is a solution yet, as I can't measure how much backlash I have at the moment. But putting some values and testing the circle test, it does deform the parts where the dents are located.
I can only verify this after my dial indicator is delivered in few weeks.
I guess I can also measure the mm though not as accurately, by scanning my circles again with a 2d scanner and using tealvince's calculation which he posted few pages back:
tealvince wrote:The value is in mm, so you can calculate the backlash from the length of the flattened section and the diameter of the circle it's on. I think it's something like (I might make a math mistake):
R = radius of circle (mm)
L = length of flattened section (mm)
E = backlash (mm)
(R-E)^2 + L^2 = R^2 (from pythagorean theorem)
Solving for E
E^2 - 2 RE + L^2 = 0
a = 1
b = -2R
c = L^2
E = (- b - sqrt( b^2 - 4ac )) / 2a (quadratic formula)
E = (2R - sqrt( 4R^2 - 4L^2 )) / 2 (plugging in values)
E = R - sqrt( R^2 - L^2) (simplifying)
So if, for example, for R = 80mm, and L = 20mm
E = 80 - sqrt( 6400 - 400 ) = 2.54mm
Correction: rethinking the geometry I think I was off by a factor of 2 on L. It should now be correct.
When I type stuff like 2 or 3 mm, I get a lot of deformation.
And when i calculated for myself, I got 4.57mm which is even worse. I'm probably caluclating something wrong.
E = backlash (mm)
R = circle radius
L = length of flattened section.

E = R - sqrt( R^2 - L^2)
E = 82 – sqrt( 6724 – 729 ) = 4.57
"M99 X0 Y0 Z0 E0" (default):

"M99 X0 Y4.57 Z0 E0"

Too much
And here's it decreased 10 times,
"M99 X0 Y0.45 Z0 E0"

Still a bit much. But seems with correct numbers it could fix backlash.
EDIT: Damn used a wrong scan (old). My backlash is actually around 1.96 mm with this formula.
But even that is too much as I even tried 0.45 in the last photo.
Solidoodle 4