I would go with a JB Jr. I've never been a fan of the L'il SD, as much as I love the full size (humbucking) version.
To me, the LSD (appropriate name!) sounded a bit overly bright, and a touch weaker than the JB Jr; ie, not as full sounding. A friend of mine had the LSD in his guitar, which was alder, and swapped them out for JB Jr's, and I thought it was much better.
Don't know how it would sound with poplar in particular, tho.