Sounds like the drivers for the LED’s are to blame. You could try buying strands of LED lights, the ones that have a bunch of 5050 size LED’s on a strip and are often embedded in plastic for protection, and keep the driving circuitry somewhere outside the shed or in a shielded location.

Avoid led strands that have any control circuitry built it. Also stay away from individually addressable RGB type as they often have some microchips built into each LED plus operating them in any type of blinking/strobing pattern (unlikely given what you’re looking to do with them) would potentially create minor RF.

They make bright white and yellow white LED strands that put out a good amount of light. You’d need several strands to replace spotlights but it could be done. The important thing is running the extra wire to keep the drivers outside of your workspace and/or isolating the driver in some kind of Faraday cage.