I had a chance to play the "Bass of Doom" once-- I was pretending to be a member of the stage crew at my college so that I could get a chance to talk with him. (He was playing with Herbie Hancock). It's a long story. I got to be alone with him in a room while he warmed up, and he taught me how to play the entire "Portrait of Tracy." He also said, "Man, I've gotta practice... I can't pull off half the stuff I used to..." Later that year (1977) I went to Fort Lauderdale to hang out with him and his family for two or three days, and get a lesson or two. He was a VERY hospitable and warm person, and his mental and drug problems weren't yet in effect. It's true that until he became ill, he was a dedicated family man who deliberately sought to become famous in order to provide for his family. From getting to know him a bit, I believe he consciously created the "Jaco" persona along the lines of his perception of the classic "rock star." A fascinating character.
Anyway, for the soundcheck at the Hancock show, he used his fretted bass, and he asked me to guard the fretless one. I confess that as soon as I was by myself I did pick it up and play it for a minute. I remember it being lightweight and resonant, with low action.
He told me that the Jazz Bass bridge pickup was absolutely essential. I brought my P-Bass to Florida, and he told me emphatically that I should either get rid of it, or add the Jazz bridge pickup. (Which I did about 5 minutes after getting back home!)
On other occasions, he claimed that his bass already had scars on it when he bought it secondhand. (This was BEFORE he entered the period of his career when he was throwing it around.)
Finally, the "of doom" thing wasn't just reserved for the bass. He tended to be quite hyperbolic -- "This wine is the best in the history of the world, man!!" and he used the "of doom" suffix to describe many things.