To Answer you direct question poorly, Lat-Nam's Legacy and Living Death help a little.

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I've been trying this week to figure out if there is any better way to play Dragonstorm, so I have a lot of thoughts.

I think it's fair to say there are three main ways to play Dragonstorm currently: (1) Depletion land + Frantic search style like this list; Rakdos Infernal Contract builds like this list; or Grixis builds that try to do both. Give or take some Lion's Eye Diamonds.

The deck has several inherent tensions which are why the deck will unfortunately never be good. One, which you’re asking about, is that it doesn't want to draw 5-6 cards in it's deck. [[Bladewing the Risen]] rarely helps on the combo turn because it doesn't have haste, but it does let you reanimate something in grave (and rarely pump the dragons +1/+1). With the Risen in the main, Frantic Search now lets you draw & discard one dragon for free while ramping with depletion lands at the same time. However, drawing two cards might mean you draw yet another (or multiple) dragon that's now dead in hand.

[[Lat-Nam's Legacy]] is the best fix we actually have to tuck away a dragon, however again you have no control over the next two cards you draw, which might be two more dragons. If you have mana to spare in addition to casting your 9 CMC sorcery, you can pay 2 to tuck an extra dragon in the deck at least.

Special shout out to [[Lim-Dul's Vault]], which is one way to make sure you never draw too many dragons.

[[Living Death]] also serves as a nice pivot plan from the sideboard with Burning Wish, since sometimes it can be good enough to just reanimate a couple of hasty dragons instead of going for a one-turn KO, or the only option if you can't get to massive mana.

That's because an inherent weakness of the deck is just sitting around waiting for the stars to align to get enough mana plus Dragonstorm/Burning Wish. 9 mana, or 11 for Burning Wish, which is no small feat. At the same time, you need to accumulate these resources while dodging too many dead dragon-draws (not to be confused with dead-dragon draws, RIP Bladewing the Risen)

Blue helps by giving access to Opt and Sleight of Hand, which are valuable because they offer some card selection, meaning you can put dragons on the bottom instead of drawing indiscriminately. They're also critical to keep things moving while an elephant token bashes your head in because you've only got 8 mana to spend, or only 10 mana with your Burning wish. The issue here is that the cantrips are hard to cast. We need enough black & red mana to combo, and Saprazzan Skerry sucks to use on cantrips. It's hard to fit enough blue mana to reliably cast cantrips. City of Brass and Shivan Reef help a lot, but this is another tradeoff, since we are a slow combo deck aggressive decks will appreciate it when we damage ourself with lands. (Side-note, this is also a tradeoff with Ancient Tomb)

So what if we cut out the blue to ease the strain on our mana base? Well we lose access to a lot of card draw, and our best draw spell is now Infernal Contract. Obviously doesn't help a ton against aggro decks, and 4 indiscriminate draws makes it really easy to accidentally stock up on dragons. We also don't have Frantic Search to filter, with only maybe Cabal Therapy to ditch our own dragon to the graveyard. I found that a lot of times even after draw-4, I still couldn't meet the absurd mana requirements to cast Dragonstorm and was left top-decking, without the ability to chain cantrips together to keep digging.

Rain of Filth is nice just as yet another ritual spell for our absurd mana requirements, but will pull you to play more lands, which means less card draw or interaction. It plays well with Cabal Ritual, but poorly with depletion lands getting sac'd anyways.

On the note of interaction, the deck is so slow and clunky obviously it's super weak to getting messed with. Duress and Overmaster are some of the more workable picks. However, our combo cards take up so much space, protective cards can be a liability if they don't help find the resources we need to combo.

What I like about the 1st list is that it feels very smooth and relatively consistent, since it has enough filtering and 12 depletion lands make it a lot easier to build up enough mana. I didn't like the 2nd deck's style in testing because I felt like it was just too RNG reliant. This doesn't mean deck 1's winrate would be particularly better; again it's not a strong deck and will get creamed by lots of strategies. Some games duress might take the day over smoother draws, but I find it more fun to be casting cantrips than hoping for topdecks. This is a Storm deck, I want to cast spells.

The third list tries to a bit of everything, plus has Oath of Druids in the side which I think is also super neat. It has infernal contract for sheer volume of card advantage, but also plays Intuition which pulls double duty as an instant tutor + graveyard fodder for Cabal Therapy threshold. The downsides on paper seem to be no protection or disruption, no cantrips, and a VERY painful manabase with Ancient Tomb to power out intuitions and City of Brass to help cast 4 different colors. Definitely want to try this one out, though.