I was pretty much on point with our DM handling the jungle exploration aspects of Tomb of Annihilation, or rather, giving up on handling them. According to him, as is typical of 5e sourcebooks, there weren't rules on how to calculate various conditions, so it was basically a "make it up as you go" sort of thing. Along the way, we've acquired enough items and spells that most of the jungle hazards are no longer a threat. Our ranger can forage food for us every day, the alchemy jug we found gives us enough water every day (and if we need more, we still have rain catchers), and with the wizard having Leomund's Tiny Hut, we can get a long rest without having weather interrupt it. So now we're just exploring without issue unless something noteworthy comes up, like crossing a desolate area that can't be foraged in.
We've also added a paladin to our party because we've got a new player, and so far everything seems to be going smooth since the player is a lot like the rest of us. Glad for that, I'd hate to be one of those horror stories. I still intend on aiming for a decent amount of healing spells since the others are primarily concerned with combat, but I feel a little less pressure to. Our party is basically a small army now; between five PCs, two higher-level NPCs, and a triceratops, we're doing pretty well. I'm guessing the DM's probably going to scale up the combat encounters from here on out, though hopefully he doesn't accidentally overdo it.
ETA: If I were going to give advice to someone planning on running this adventure, I'd probably tell them to do away with the survival aspects. The hexcrawl already takes up a decent amount of the first chunk of the campaign, and that's with just the basic "are you lost/can you chart the hex/did you get a random encounter" rules. Throwing in weather, disease, and excessive inventory management adds a bunch more things you need to roll for and keep track of, and it quickly bogs the game down.
If you really want to try, then make sure you run through the basics with your group before you get started, and see what they think. Maybe they'll be game too, but if not, don't feel like you should do it anyway. That sort of campaign appeals to some players, but not all. Yeah, I know, maybe most players are pussies that don't know how good they have it, but if WotC isn't going to bother to create a decent survival system for their adventure, it's probably not worth bothering.
If both you and the players agree, then this is one campaign I would highly recommend doing digitally so you can stay organized. My DM might have been overdoing it a bit, but he had pages and pages of notes behind the screen at all times (no I didn't look but it was hard not to notice). He at least did the map digitally, so that was smart. But if you find it's getting tedious and not fun, don't be afraid to drop the survival stuff so you can stick to the meat of the campaign. As mentioned above, within a few levels, your players should have the resources to avoid those hazards anyway, so you're really not losing much if you stop keeping track early.
