The electronic variable speed lathes as well as the mills need treating in the right way and they are then quite capable. If you try and apply methods based on heavy old iron with belt or gear speed ranges they are not a t their best with the slow heavy cuts. better to run them reasonably fast and take a lesser cut which gets the job done in a similar time as you are feeding a lot faster.
I’m not sure you will have much luck finding a slotted cross slide for that size machine, looking around at similar from Warco, Amadeal and Optimum they all seem to have the same arrangement that you show though none of them have a really good photo of the cross slide.