All I know about these two is that their roots are extremely soft and are VERY sensitive to any disturbance at all. As for being invasive,the leucadenron can get quite large, so it may have a extensive root system. Both need really good drainage as they're susceptible to root rot on occasions, especially the leucadendron. I'd plant it in a spot where it has excellent drainage, and as far as practicable from your house if only to avoid any root disturbance...Pomaika`i! :-)

Neither has aggressive roots, but both are very sensitive to root disturbance, and also do need very good drainage, acidic soils, cooler nights, and no phosphorus in the soil. If you previously had other plants in the same area that were fertilized with complete fertilizers containing phosphorus, you may have problems with root toxicity. Also you should be aware that Leucadendron argenteum is not a deep rooting tree, and is often subject to blowdown in high winds, especially if planted out as a larger container plant, or if it has any kinked roots. Phytophthera fungus is a real problem with this plant, especially if it gets water or rains when the soils are warm. I would imagine you must be in the higher elevation protea growing zones to even succeed with these in containers, as they don't really like tropical/subtropical conditions.

Aloha Colvillea and Bahai. Mahalo for your responses. It seems root disturbance from planting may be as big a concern as site selection. I'm now confident about the location I've selected, but will need to devise a delicate method of planting. Ho'omaika'i!