The problem here guys is its darn near impossible to solder anything onto Aluminum. I have ditched/scrapped DIY projects mid-stream because I could not get solder to flow on to Al. OP I think you might be able to solder the spring onto the brass pill on one end, but the other would need to make touch-contact. If you could DIY fabricate a copper or brass ring, press that into the throat area of the light and wire-connect the pill to the ring with solder I think that would be better.
Side note... IMHO springs that are used to bridge large gaps are generally a bad design. The only time I see them advantageous is with Incans, where heat conduction is not an issue, and they need some degree shock-impact isolation. Just the other day I had to fix a poorly designed tailcap that used a spring to bridge a gap between the retaining ring and pill guts.