When I said the great taurus was the only fast element in your army, I forgot the bull centaurs, but they pack enough punch to charge a fully ranked unit (but I would strongly advice against doing so from the front) and win while the Taurus can only take on easier targets but is more mobile.
Be sure the great taures, black orcs and bulls centaurs will be priority targets if he can get a clear shot.
I understand you want to make an army that feels different from the dwarves: monster, cavalry, magic… but you need a plan against two typical dwarf armies: the shooty dwarves who will outgun you and the close combat army that has better troops than you due to better armor, better WS, runic support. Since you already have few range units, I’d say you can swap magic to have more bodies to either soak up to damage when you march toward them (you’ll prefer greenskins dying rather than chaos dwarves) or more units to force them to show their flanks.
For the wizards, go bigger (6 levels) or let them at home. You pay 300pt for 6 casting dice (that you can boost) while he gets 4 dispel dice for free. You can’t base your strategy on you ability to force him to move due to magic and a single warmachine.
Smaller hobgoblins units may be useful as a screen, in this case keep them cheap. They’ll flee at some point. Feel lucky if they flee once they have been charged, you just disrupted his formation for a cheap cost. Remember that your general will be far away, so the leadership of greenskins will be lower: 5/6/7/8.
I am personally not a fan of archers against dwarves. They are useful against light expensive troops, glasscannons (light cavalry, light flyers, heroes on pegasus, wizards, warmachines crew, daemons, elite elves, ogres…) not against tough troops in heavy armor.
It they are shielded and armored, they provide ranks and numbers without taking mass casualties from most enemy combat units while your better troops provide the killing power. They can also move faster giving flanking opportunities.
The lore of Metal is quite good against dwarves because of their good equipment, runes. It’s mostly debuffs and some missiles.
The lore of Fire is usually direct damage.
The lore of death does mostly damage, some of which with short range and no save.
The lore of shadows is more versatile, buffs, extra movement and a bit of damage as well.