My buddies and I have built 3 of these cummins trucks. Yes the 78 grille will fit. On my own truck I used the 92 diesel rad support and swapped in the 72-76's headlight mount sections. I also had to swap in the 72-78 hood latch but you won't need to if you just use the 92 hood.
These swaps work really well. I've been driving mine for many years.