I wonder though if the SWR van go below 1.5:1, or if the minimum impedance of the design precludes that..?
The matching section of a J-Pole or a Slim Jim is a variable impedance transformer. At the bottom of the U, it's 0 ohms. At the top of the U it's around 3000 ohms. The coax attachment point is somewhere between the two ends of the possible range of impedances. Down near the bottom of the U but up the range somewhere there is a 50 ohm spot. If you attach your 50 ohm coax there, it will be a 1:1 match.
It usually requires experimentation to find that spot the first time.