As I see it, it is always the safest option to have the nav aid on which you are navigating displayed on the PF side. In this case, about 6 dme outbound I would select HDG then tune the ILS and use PNF display (still VOR/DME) to determine base turn point. After commencing the turn, have PNF tune ILS, then set up as normal to intercept and track the ILS.
I suppose it would be a good idea to see what your company SOP says!!
