The Exorcist itself doesn't have that many shiny bits, honestly. Ok, it's a pretty shiny model, but it's less of an issue outside of that badly sculpted organ. When I was painting mine I found that yeah, you want gilded areas around the front and side murals, and some of the keyboard area, but what gave more trouble was painting the figures in the murals itself (painting surfaces a flat, consistent white is hard, harder than getting a consistent metallic layer).
But honestly, if you layer (and thin) your paints even the gilded areas aren't that obnoxiously shiny. Try going brown -> brass -> gold for a more muted look that'll go better with the rest of your model. You can even go for bone -> white for the pipe organs if you don't like the shiny stuff that much, so that it looks more like ivory than metal, and layering on white after the bone means that it'll be a different colour from all those purity seals. IMHO with the Exorcist sculpt, particularly with the organ piece, the model isn't detailed enough for you to wash and give the metallic layer some depth with false shadows, which makes it look worse than usual if you go full on brass on black. That's why if you look at a lot of GW's own models of Exorcists they tone down the metallics heavily and paint on their own shadows.
Additionally, the Exorcist isn't a battle-tank. You don't want to be running this up in the front lines without a screen of sisters, this isn't a Leman Russ Demolisher. Sure, if you want to paint dirt and grime on the front or have a dead heretic smeared across the dozer blade or something, go ahead, but on tabletop please hide it behind your sisters and fire from 48". That F 13 is deceptively weak.