I've never played the bass in question, but didn't the fretless groove tools come from the factory with a synthetic fretboard? If that's what you've got you should be able to use any strings without worry. If you've got one that was de-fretted by a player, that's a slightly different story, though purpleheart is a fairly hard wood anyway.
I ended up going with the Kalium roundwound 0.136B - 0.029C set, plus a 0.182F#. The nut needed some minor adjustment with a round file for the F#0 string, and the tapered end needed some persuasion to feed into the bridge. First time tuning the strings, the C machine head snapped, so I ordered two sets of Gotoh 4-string tuners to replace them.
I also confirmed, after going through some photos, that this is a de-fretted neck: it has the same top-edge inlays
between the fret lines, which is disorienting for someone used to playing with dots directly on the fret lines. Eventually, I'd like to add some white dots at the proper positions, and black out the inserts and fret lines. (Any suggestions for materials or techniques?)
I looked into replacing the neck with an original fretless neck, but since this bass was manufactured in China under license, Conklin says I need to contact the company that handled the licensing for parts; and that company says they no longer have any parts for it, so I need to contact Conklin.

So unless someone knows where a fretless neck for this bass is sitting around, I'm going to have to "finish" the conversion of the de-fretted neck on my own.