Welcome to the forum! Thank you for providing the additional details!
To confirm, you changed alpha_homing_direction to home_to_max and inverted the alpha_dir_pin to 0.5! in the configuration file?
Check that your Device Origin is set properly. In LightBurn, Edit > Device Settings and set the ‘Origin’ to the front left (lower) corner. This is separate from the homing location. Disable homing on startup in the LightBurn Device configuration. Then the head should not try to home when you connect in LightBurn and you can try jogging around.
Place the laser head in the center of the work area and power on. See if the head moves the correct way (left / right, and forward / back) as the jog buttons you are pressing in LightBurn. Are they moving as expected? Please report back with the results for each direction movement attempt.