What is a slab bass? One without a tummycut? Because I would actually really like that.
Fender made some low-budget Precision basses in 1966, primarily for exporting to the UK. For some reason Rickenbacker also shipped the budged 1999RM bass to the UK at the same time; I guess we were cheap back then. I guess the economy was so wrecked after WW2 that it took a while to recover, there was a trade embargo on US goods until the early '60s...
The Slab bass is exactly as you describe. It has all the fixtures and fittings of a post-1957 Precision bass, but without the tummy and forearm contouring. I can only guess that they took the body blanks, routed them for a neck pocket and electronics cavities then chucked them straight over to the paint shop rather than spend the extra time giving them a nice round-over or contouring.
The pickguard isn't the usual Tortoiseshell affair either... apparently they sound different to a stock Precision bass. I'm not entirely convinced, given that they share the same circuitry, and I think that because the bass is synonymous with heavy players, such as Ace Kefford and John Entwistle, people perceive them to have a more aggressive tone. In the case of John Entwistle, he used a different bass at the 1970 Isle of Wight festival (a stock, black, Precision bass) and it sounds different on the recording. Because the recording was captured in the (muddy) field there is a certain element of uncertainty to the proceedings. It could be that John had to borrow the bass, or had bought it that day, and therefore not set it up accordingly.
When I think of the classic 'Slab' tone, to me it is all about having stupidly low action. With an overdriven tube amp, what is usually classed as undesirable fret buzz becomes a wall of musical and tightly marshaled upper-harmonic content.