According to this old thread I bookmarked, a 4K export (even with 1080p source clips) at a very high bitrate is the trick: Why I transcode to 4K and fast bit rate
(Note that “fast” bitrate is a strange description.)
Consider to use HEVC or VP9 WebM to reduce bitrate/file-size some (60% of H.264 bitrate is a safe level). Previously, I had suggested 80% VBR, and I think that may still apply regardless of video codec choice.
In Shotcut you can make a project at 1080 and export it at 4K as long as you do not use any filters that involve coordinate positions and sizes such as Rotate and Scale, Size and Position, Overlay HTML, Text, or 3D Text (Crop is OK). If you need to use those, then export at 1080 using an intermediate or lossless preset, open the result in the Source player (double-click the completed job to open it), choose it in Export > From, choose a preset, and change the resolution in the Video tab as well as any other export options.