Is there an issue with splitting up papers already posted on ArXiV?
No, you shouldn't replace the old paper with the new one.  Replacements are supposed to be revisions, not &quot;very different&quot; papers.  The replacement that you propose would not only revise your contributions; it also looks like an attempt to erase your coauthors' contributions.  The change in authors would almost certainly raise a red flag with the moderators (through arXiv's auto-moderation software), and I expect most moderators would reject the replacement.
Submitting a new paper whose text significantly overlaps an existing arXiv preprint will also raise a red flag with the moderators, but as Dan Ramras suggests in a comment, explicitly acknowledging the overlap will convince most moderators to accept it anyway.
(I was an arXiv moderator for over a decade.)