How can I scale a 4K external monitor to have a comfortable amount of space
Using Retina mode on a 4k display is a performance demanding task - especially for that 13" MacBook Pro. When you choose "odd" resolutions like that, the operating system will have to render in really high resolutions and down-sample to get an output suitable for your monitor.

What you could do instead was to install SwitchResX, Display Menu or similar apps that allows you to configure the monitor to your liking. I would recommend trying to disable Retina mode and simply use a high resolution with the monitor (not 3840x2160, but something smaller). 

If you disable Retina mode, the performance demands are considerably less.