You did first step correct - you converted splines to lwpolylines... Then I've found that small gap that had to be connected, then I applied (c:bbpoly&hatch)... It seems that its OK... See DWG in attachment...
BTW. With splined geometry, hatch is I suppose complex to (entmakex), so you'd probably have to use commands, and beside that SPLINES derived from boundaries don't look quite perfect - look around intersecting vertices... See DWG in attachment...
HTH, M.R.