There are a couple fundamental differences between Warrior Priest and RP/AM
1) Righteous Fury. It is the fuel used for heals. It is only filled up out of combat, the spell supplication (10 second cooler and is horribly inefficient) and smacking people. Smite is the primary smacking tool, because with each [spell]Smite[/spell] (vs many opponents) it is possible to practically fill the whole RF bar.
2) Buffs. Warrior Priests have an excellent melee-buff [spell]Sigmar's Fist[/spell]. However, it requires us to smack people.
3) [spell]Touch of the Divine[/spell] has a 1 second cast. Yes, the group heal has just a 1 second cast.
4) WP's don't have any lifesaver spells. ToD is the only direct heal we have, everything else are HoT heals.
All this means a WP is intended to keep the on casting ToD for ever, and the WP actually *can* do that. But it requires him to be up front with the melee dudes. For a WP AP's are not an issue, and RF is not an issue as long as the cycle of ToD-Smite-ToD-SigmarsFist can be repeated over and over. And if you look at the cooldowns, it is pretty obvious this is in fact the "intended" cycle for WP's.
So, please, do *not* assume a WP goes up front to be able to cast a lifesaver. There are no such lifesavers in the arsenal. The WP is intended to be the source of a steady and infinite basic healing. When RP and AM have been AP dry for an hour, the WP just keeps going on like the Duracell rabbit. Every three seconds a 400 heal to everybody in the group. It is not enough to keep a tank alive in front of a hero, but it is enough to keep tanks facing champions and players alive, and it is a solid basis of healing for the one tanking the hero which provides the RP or AM time to cast their life-saving heals.
It is important that a RP or AM is available to provide direct healing to the tank facing the hero. Throw in a group heal if needed, but to really supplement each other, the WP needs the RP/AM to take care of the "oh shit" heals. The WP's only "oh shit" button is the group shield, and it has a 60 second cooler, and IMO it is best to be used when the charge upstairs start (there will be a few seconds of chaos and mayhem when the tanks grab their targets, and if somebody throws a heal before the tanks have got aggro, everything will go pear-shaped) to provide that extra little time to get everybody in position. RP/AM need to be sure they don't run AP dry, because they are the ones who will be saving lives.
So, to iterate, by all means do stay downstairs and cast group heals for those upstairs, but the problem is then there is no life-savers available then. WP is *not* a lifesaver class like RP or AM. WP cant save you from the brink of death, because there simply are no such heals available.
Thus the WP needs to be up there with the melee, and to get maximal efficiency of the WP heals, he needs to be in the group being whacked hardest (one additional benefit is the armour bonus from the [spell]Prayer of Absolution[/spell], but I suppose everybody has by now figured that out

). But there *has to* be a RP or AM with a LOS to the tank facing the hero.