I have created a map with a single layer that needs to be exported for printing (30 dpi quality and quite large). I researched this extensively and see that the ability to export an image has been deprecated in the new Carto Builder UI. How should I proceed with getting this exported?
I think you mean 300dpi...
If you're data lives in CARTO and you want to print high quality vector graphics, I suggest using the QGIS plugin offered from CARTO:
This will require you to do some re-styling of your data, but you should find similar styling methods in QGIS as in CARTO
Then you can create a print composer at the correct size you want to print, orient your map, and run off some PDF's to see how the linework comes out at the scale you're plotting.