mirror backplot

I've had this CNC with a closed-loop DC servo for a long time, and it works well for both movement and backplot with the home dot at x0 y0 as seen in the photo. The only problem is that it only works well with the y-axis inverted; the y-axis moves away in a negative direction. I decided to set the axis to positive as the x-axis, but the home dot moves to the left, and I haven't found a way to set them in step... basically, the plot moves outside the work area. Could it be that I changed the order of the pwmgens to match x and spindle on a 7i40hv and y and z on another to use two different voltages for the motors?

Here they are, I changed TCL with a modified one but it's not its fault, it does the same with the original one.

Tom, I tried everything, inverted the home encoder phases and all the possible settings... if I set the correct axis (reversed) everything is fine but the plot is mirrored and home moved to the left outside the frame.

In the screenshot of the first post the view is that of the real machine, with x0 y0 at the top right but y moving away becomes negative and if I modify the axis to make it positive, home moves to the left and the backplot is mirrored.

I'm definitely wrong because I was a machinery repairman. I started in the '80s with Olivetti CNZ machines, all transistors with delay lines. The last 20 years of work have been spent welding and cutting. I built a small CNC and a plasma cutter for fun. In the photo, you can see the machine in the home position; the crosshead to the left is negative, and the carriage coming forward is positive. It doesn't look right because with the handwheel clockwise, one axis is positive and the other negative, it's easy to make a mistake. But if I invert the crosshead to make them go the same way, the plot is mirrored. But I don't even waste too much time on it because I have Sanmotion AC motors, so I'll do everything properly.

Linuxcnc will let you do anything but there is an expected paradigm. If you go against the paradigm, life becomes painful.
Think of the home position as being 0,0 on those Cartesian graphs you drew at school and the table represents one of those quadrants.
So if the current position is home, X & Y need to be  negative values to move away from home.

Another way of looking at the expected paradigm is that the front of the machine is where you stand at the machine. Home should be on your left and closest to you with the gantry going across your chest. So to satisfy that rule, you need to stand at the back of the machine behind the gantry.

So you could
1. stand behind the machine
2, Turn the machine around so the back as shown is the front of the machine
3. Live with negative X & Y coordinates
4. Move your home switches to the front left of the machine
5. In your homing configuration, set the home position to max-X and max-Y coordinates so it knows the home switches are at the back of the machine.

I might add if your origin/home respects the cartesian origin and you accept the quadrant you are in, it all becomes moot when you place your workpiece on the table and set the part origin with G54 offsets. Once you touch off, everything is referenced to the part origin.