Simple linear interpolation should suffice for the given purpose, that is latitude $\alpha$, longitude $\beta$ maps to $$\left( 800\cdot \frac{\alpha+1.8792678}{1.8792678-1.8783669}, 600\cdot\frac{\beta-57.45827}{57.459293-57.45827}, \right). $$
Simple linear interpolation should suffice for the given purpose, that is latitude $\alpha$, longitude $\beta$ maps to $$\left( 800\cdot \frac{\alpha+1.8792678}{1.8792678-1.8783669}, 600\cdot\frac{\beta-57.45827}{57.459293-57.45827}, \right). $$