Let me try to recap (!), saying some things that so far have perhaps been taken too much for granted:
1. The NAD is a much better piece of equipment than the Pioneer. Unless you need/want the tuner section of the Pioneer as a source or as a part of your AV system, there is no point in keeping it in the system, especially not as a preamp.
2. You need three sets of line-level ("pre-out") outputs to feed your twin amps and sub. A 1 --> 3 way splitter will do that without major issues.
3. Cable the splitter into your single pre-out from the NAD, connect one splitter output to one of the Anthems, another to the other Anthem and the third to the subwoofer and you are done.
4. Sell/donate/store/burn the Pioneer, unless you need a radio.