(extended answer- may be useful for identifying other limitations)
To be honest I can't actually be 100% certain if this actually fixes it as it's still a finicky process and only the beginning of potential problems imported Sculptris textures bring (overall, sadly, I would simply not recommend it at all).
The immediate issue may be a difference in IMPORTING the texture as opposed to simply assigning a texture the "traditional" way via UV editor. It is possible the issue is one also imports a set of "coordinates" within Sculptris to correctly map the texture on the corresponding mesh, while the other fails due to the lack of marked seams on the UV map that Blender tends to require (resulting in a randomized mapping spread across the mesh). Of course, applying seams appears to run into a vastly greater problem that it tries to superimpose the neat 'unfolded' Blender mesh onto a fragmented Sculptris texture image- which makes the issue even worse.
Keep in mind, I haven't been able to certainly differentiate this as the issue, as it appeared to have been a random consequence the first time I used what appeared to be a similar approach each time.
BUT, to make up for the lack of decent answer to that issue, I think I may have found an answer to the UV-unwrap incompatibility; my suggestion is to try to make some duplicates of the object (low-poly ones) and flatten them so you can see a broad, flat representation of pieces of the texture, take screenshots and attempt to assemble an improvised texture using these in another program (Photoshop is an obvious choice, Krita should also do the job perfectly fine too).
I regret to say the main take-away message is I STRONGLY encourage anyone who did a lot of hard work on a painted Sculptris object, to bite the bullet and start from scratch making a new Blender one, complete with a new texture. It would actually take less time and run into less problems.