Have you tried Clique (Faerie Wizard) ?
Since you're on two colors you could possibly want to try 1-2 Price of progress as a finisher (but you'd have to abandon Cavern and go -1 volcanic island). Also i'd go -1 Pyromancer or -1 Lavamancer, +1 delver, because delver is your strongest/ most consistent turn 1 play in a deck like this.
Lavamancer could possibly go in the side to fight other aggro decks.
Why aren't you running the 4th bolt ? flame jab just seems weak in comparison
What's your MD answer against Mud and blightsteel colossus ?
What's the purpose of surgical extraction in the main? is your metagame dredge heavy ?
What do you run in the side?
Mystical tutor seems nice to get Answers/ time walk.
SDT might be strong with Delver, but not with pyromancer you could probably replace it by 1 preordain to go both ways. Or you'd be fine just cutting it for something else entirely.
Your decks looks like it wants to be more grindy than Rug delver so you could probably try adding a mana denial line with 2/3 Null rods and strip effects.
That's about all I can think about. I've played around with a similar list a few times but I found that without green you're just loosing to much good answers (Trygon predator, Nature's claim, Ancient grudge) and you definitely miss the Goyfs. While they may have less potential growth than pyromancers over the long run, they are much faster.
I want to play something like RUG Delver but I don't have goyfs at the moment. I've been playing around with U/R lists that replace Tarmogoyf with Young Pyromancer. So far it's been working well.
The four cavern of souls help make sure my creatures are on the battlefield, this also means I can use my counter magic offensively. I don't tend to protect too many spells because of the redundancy in the deck. The main exception is time walk. Gush is much better than ancestral in this deck for some reason. the fact it's free and lets me replay lands is a big deal. I usually don't Gush unless I need the land drops, which usually means turn four.
Going forward:
I'm trying to add as many high power level cards as I can that are useful. Is there anything glaringly omitted?
Also, everything in the deck is a human wizard, if there's anything good in either tribe I've missed let me know.
Any other thoughts are welcome.
I have also played with a deck very much like this, and I absolutely agree about the Vendilion Cliques. Run 2-3 of it. You will not be disappointed. I also have tried Price of Progress, and it is an excellent card in many metagames, especially when you have snapcaster. Notably it also kills planeswalkers. While null rods can be good maindeck, I think it is usually better as a sideboard card versus something like Tezzeret or Burning Tendrils (Unless you really want to emphasize a resource denial plan and not be as aggressive).
I also think you should splash green for ancient grudge off a tropical island. Play one of them main. It is an incredibly brutal card against shops and disrupts Vault Key. You also should run a steel sabotage, because it is versatile and is an answer to blightsteel. You should probably cut flame jab for another bolt or a Price of Progress, because both kill jace, are instants to make snapcaster better, and can burn your opponent out for the last few points of damage. The extra one damage is rarely relevant on creatures anyways. I'm unsure about lava dart. If it is a good card for you keep it, although If it were me I would cut it for a price or a bolt to be more aggressive.
I agree with Whitelotus' assessment of SDT and surgical, although I will note that SDT is very effective against shops(Which is usually a good matchup for you anyways If you have a little maindeck hate). 3 or 4 delvers are both suitable amounts, because they flip less than in Legacy RUG or UR.
On the subject of caverns, I don't think they work well enough. I understand that you want to use your countermagic offensively, but if you win a counter war then they are out of countermagic anyway, and you've managed to apply some pressure to the board. If you are worried about losing counter wars you can add 1-2 more missteps. Adding wastelands and a strip mine will be more relevant if you still want a utility land slot. They don't activate Gush but they can also really screw your opponents over, and you have enough colored mana.
This is a very fun and versatile deck. I hope you enjoy it.