I had once upon a time considered the JB, but backed off. I found the Custom Customs actually a bit unbalanced away from the low end for my tastes, but did think about the Custom 5 when it came out. Still, I was already a bit soured on SDs by then.
I ended up going for BKP Crawlers, which I think would do a reasonable job of meeting the requirements for "clean, warm, thick and open sounding". They're not particularly low output, but then neither is the JB or Custom Custom! The Crawlers (and Nailbombs) are around the same range as those: 14k-ish to 16k-ish, no?
If you really want something of a lower, PAF-like output, you might want to go for the (and this is the BPK "stock answer" ;)) Mule.