If you have divine protection and become near death from a timed instadeath or low HP, some or all of your protection may automatically convert itself into a cure: “You suddenly feel the power of [deity] surround you! You feel limber/cured/much better/etc.” This should probably work for a narrow range of symptoms (probably not HP loss, possibly any major trouble), and the help delivered should be strictly worse than a prayer if possible (because having this trigger will not affect your prayer timeout).

It should also probably not work in Gehennom, and a key factor is that it should not be reliable, either. Possibly, also track which gods you got it from; protection from donating to crossaligned gods (especially Moloch) will trigger less often.

A slightly more extreme version of this idea is to make divine protection no longer grant AC at all.