What would you have done if you were 1 of the other 3 tanks? Do you really die often because of healers not healing? If not, it means that you're always playing more efficiently when you're playing other tanks (not that it matters). I think much better move would be to only use your "immortal" oGCD when you panick if it's off cooldown (HG should be used on cooldown tho for big pulls) and otherwise just trust the healer, unless they've proven that they aren't to be trusted.
Trustworthy until proven untrustworthy makes more sense imo as a mentality because you have no choice but to trust healer in most party compositions (when there's no PLD/RDM)