I don’t know how far along you are with planning and gathering parts/materials for the build. Do you have a specific LED you want to use? If not, let me recommend the Osram KW CSLPM1.TG, otherwise known as the 2mm² “White Flat”. It is slightly rectangular already, and quite throwy when used in the right configuration. If you put it behind your cylindrical lens in the same orientation as the lens, it will amplify the “spread” factor a bit compared to using a “normal” square die or a round die emitter.
So, if your emitter is like this………
and the lens normally does this….
then you will effectively get this….[]
You can read about the “White Flat” emitters HERE if you haven’t already done so. 