Power doublers that stack with double strike such as Two-Handed Axe, Gisela, Blade of Goldnight, and Inquisitor's Flail are pretty useful if you need Shivan Dragon to be huge.

I like how Unquestioned Authority offers unblockability while replacing itself. War Cadence offers a combat trick you can use to help get through.

Dawnbreak Reclaimer and Pulsemage Advocate are repeatable ways to recur your Dragon, there is also Gift of Immortality.

A nice spare Ghostly Prison effect can be found in Kazuul, Tyrant of the Cliffs or Sphere of Safety, there are also Baird, Steward of Argive and Windborn Muse. In a pinch a card like Spurnmage Advocate or Intrepid Hero can make good deterants.

Vs running so many 1 colour wards have thought about Flickering Ward? You can run various tutors that can find it or another Enchantment such as Heliod's Pilgrim or Moon-Blessed Cleric, there are various spells that can do the same or better, plenty can also find equipment. If you do stick Flickering in you could also try Mesa Enchantress, which is also great with enchantments period.

With access to Pro Red, maybe some Red wipes that use damage? Some include Blasphemous Act, Chain Reaction, and Reckless Endeavor, Pro Red makes these 1 sided.

Hope some ideas here apply, I typed this fairly early in the morning, with only so much coffee, so forgive me if this is a heap of spam!

The main problem I see is how you plan to reliably play Shivan Dragon and keep it in play. As he's your hidden commander, I would suggest splashing black. Black will let you reliably tutor for him and allow a couple/few recursion spells if he's killed. An added bonus of adding black is you also get to run Crux of Fate as a solid board wipe and Kaya's Ghostform as another protection piece.

A card to consider for the deck itself, is Leyline Tyrant. His red mana storage works well with Shivan's Firebreathing.

Edit: As a side note, you could consider running Shivan as your commander with a white background under a rule 0 situation. This would admittedly make him more difficult to play, it would solve the 'finding/getting him problem.'

There are some ways to tutor out the Shivan, one is Gamble, another is Magda, Brazen Outlaw. Gamble works well with recursion effects, which is a niche area for White. Zirilan of the Claw is a really weird one, iirc you can get around the exile effect by flickering the Shivan, at which point it's yours forever. Flicker effects are sometimes useful to protect the Shivan, so they're not 1 trick ponies and you could run more than one in a deck without them being superfluous. The worst might be Magda, but there are ways to generate 5 treasures and that's all you need, and some dwarves have amazing tap abilities like Dwarven Miner, a move that will annoy your opponent without really winning you the game, it's using your opponent's lands to dig out Shivan. Another good Dwarf could be Dwarven Blastminer, Dwarven Driller, Storm-Kiln Artist can make treasures too, some maybe options are Axgard Cavalry, Bomb Squad, Dwarven Armorer, and Mine Layer. There are some terrible options but I'm not going to bother with them. If you want a pretty competitive feeling Shivan Dragon deck, you might look up some Magda cEDH lists, that's a fairly competitive way to dig out a non-Legendary dragon.

Green is another great colour to look at if you want to dig out creatures, if you used something like Atla Palani, Nest Tender you can dig out creatures from your deck, guaranteeing access to Shivan eventually (if you run very few creatures you only need to pop a few eggs and you're guaranteed to hit) and she'd give you access to Green, which has it's own power buffing effects that can be quite notable. If you throw in a few cards that shuffle your graveyard back into your library (Green is great at this), you can recur your Shivan through Atla, so it can be pretty resilient.

I'm not disagreeing with Black as an option, just throwing another idea out there for you to think about.

The coolness of this deck idea makes me vaguely curious about a Red heavy Dragon Tyrant Atla Palani deck, just run stuff to make a nutso Dragon Tyrant and take over with your beefy beater.