@The Aluminum Falcon
You are right, I wanted to use a wipe, but I am new to Kdenlive and video editing in general, so I didn't know how. I've set the transition to Wipe, but I still did not get the desired effect. Only now I realised that I also need to select a luma image file for the true wipe effect.
Problem is, there is a diagonal wipe just a few seconds later, so having 2 wipes only 2-3 seconds apart looks odd, so I may need to keep the crossfade. Or at least use an extremely soft wipe, sort of a blend between wipe and a crossfade.