The nutrient levels in any compost are typically low enough that high levels of phosphorus are unlikely to be a concern but it does depend on the original ingredients used to make the compost. Generally, high levels of phosphorus are the result of using fresh or unaged manures or excessive fertilization. Or your soils may be naturally high in phosphorus, although that is not very common in PNW soils without a lot of amending....have you tested?

Not all of the Proteaceae are phosphorus-intolerant and it stands to reason that phosphorus is naturally present in some level in any soil, so exactly how intolerant embothrium may be is up to some debate. You'd just want to avoid a high phosphorus fertilizer or high phosphate manures (and that includes any poultry manure).

Plant in the soil you already have, mulching afterward (wood chips are the best mulch for trees and shrubs, perennials etc. large enough not to have the crowns buried if the mulch is moved sideways by bird and animal activity). Same soil texture throughout rooting area, no pits, pockets or zones of different material.

I've put lawn fertilizer on my largest firetree and had it look better afterward. The phosphorus poisoning issue may be more of a problem with specimens in containers - or any other situation where they might get a comparatively intense exposure (I lightly sprinkled lawn fertilizer around my one tree once, for the nitrogen content - which it appeared to respond to).