I have yet to be on DRG since the recent update. Its POSSIBLE that this new "Attack" breath and "Heal" breath JA has messed things up a little. Has nothing to do with ur wyvern being a lower lvl than u, as explained here that paramaters thing is just a temp thing they introduced a while ago, while u remain in the same zone and it dont die.
But really, at 75+ and uve NEVER done a HB? Plus, if u has the items, i hope u r macroing ur AF/Relic helms.
But basically, yea any spell, bar spels r good, espech /rdm, as they r self targetting and can be done in or out of a fight. Many DRGs that go /whm use Dia, great cheap spell yea, but if mob needs to be slept its a bit meh. Plus also, if theres no mobs to Dia then u has to do a propper cure. No biggie but still.
If u r serious about not HBing, like uve Astralled and Abyssea'd DRG to 75+, and u seriously dont know this stuff, Wiki IS correct. Like a few others have said, regen can mess it up sometimes, but u should be using ur helms. They r simple enuf quests (for AF) so get em done.
Casting a spell with a PROPPER mage sub (whm blm rdm blu) will spark a HB. Subbing other magic casters (such as nin) will have a lower HP threashold, but again this is all old stuff and a DRG should know all this.