Correct strategy for handling extreme undergearing

My current strategy for handling flex at 510 ilvl (don't ask) is to 100% gem stamina to provide a larger timeframe for sub-par healers to stabilise me. I'm being told this is completely incorrect but the differences between stamina and haste gemming seemed night-and-day to me based on trash pulls and boss switches in LFR and flex.

Not much specific data to work with here. Just the idea of that strategy. Is there something I'm completely missing here?

Depends on the situation, really.

Are you the only one undergeared? Then that's probably the best way to go. No matter how much Haste, Mastery, Dodge and Parry you have, you will always take some full hits, and the extra stamina will help you survive those. You'll be taking a lot more full hits, so this will be more taxing on your healers, but that should not be a problem if your healers aren't undergeared. You also deal less DPS, but again, that should not be a problem if your DPSers aren't undergeared.

Begs the question, if you're being carried, why not go DPS and let someone else tank?

Is everyone undergeared? Then the situation starts to change. Healers won't have the luxury to focus on you constantly, and you'll have to work a lot more on keeping yourself alive. Haste is especially good for that. It also has the benefit of increasing your damage output, which can help a lot on making berserk timers.

I'm currently raid leading a flex group for a social guild on a server and faction where I have no presence. The rest of the group isn't really skilled and they lack a viable tank, which is why I'm handling the task. I'm the only undergeared member there and it's proven successful so far, having gone through the entirety of flex 1 without a single issue on my part becoming apparent.

The way it was explained to me by a friend, it sounded like I chose the opposite of the correct option. Thanks for clearing it up for me.