If you like using way too many parts. ;)
There's no good reason I can see for doing the supply-pin wraparound trick for a rail splitter. The output is always at mid-supply, so you don't need the RRO capability, and it has serious disadvantages for this use.
Because the output comes from collectors, its output impedance rises rapidly with frequency as the loop gain declines, so that all you've got holding the splitter output still is the capacitor. That rising output impedance looks inductive, so there'll be a nasty resonance with the output cap that you'll have to manage somehow.
Using the complementary follower approach gets you a low output impedance at all frequencies, isn't inductive, and takes fewer parts.
But a TCA0372 and a BFC is the ticket.
Cheers
Phil Hobbs