Jace, at least the latest version, relies a lot on efficient cards - especially creatures so that he can capitalize heavily on all those clues to always have “leads” on how to even further mess up his opponent’s day.
For starters, drop all of the creatures from your deck - except for Moondrakes. Most of the creatures in your current deck aren’t fast enough to reliably play in 1-2 turns (assuming you aren’t mana locked by a poor grid) or have a more efficient option that costs less. Moondrakes’ ability to give all of your creatures flying is huge - even more so than passive +2/+2 buffers from the Djinn since this will allow you to bypass most non-flying blockers when you aren’t playing against any green decks. You do NOT want to have a full hand when you have a fair number of clues out on the board!
Creatures I would consider to use that you mentioned having access to are Daring Sleuth, Jori En, Mizzium Meddler, and the aforementioned Nephalia Moondrakes. Daring Sleuth pairs AMAZINGLY well with the new Jace, as he is almost guaranteed to transform and provides a reliable source of clues, card draw, and secondary mana battery through Jace’s first skill. Jori En is just amazing in any deck, plus a decent stat line for the mana cost. Mizzium Meddler, while a shell of his former - albeit highly annoying self, still provides a great stat line for 9 mana (4/7) and can still disrupt your opponent’s mana stockpile with some lucky cascades.
You do have the critical supports for Jace: Ongoing Investigation, Tamiyo’s Journal and Cloaked Estuary. Personally, I would keep it at that. Thopter Spy Network is great on paper… especially considering the number of clues that are going to be thrown out over the course of a game… but I would rather have another spell for Jace here. Especially since there is this thing called a “carriage” and you’ll probably want to have something to deal with it should it show up…! By Sphinx’s Revelation, don’t you mean “Sphinx’s Tutelage?” For 6 mana, this stinker will literally put your opponent on a mana treadmill as long as you can keep playing out your hand.
For spells, Turn to Frog is one I use (and why not - it’s amazing!) - however I never considered using Helm of the Gods. Could be a good way to boost my team to keep certain creatures alive, especially after I use Haunted Cloak to get them blocking “carriages.” You’ll also want to add some form of a mass-bounce spell as an insurance policy in case things go really bad!
The deck I run right now is as follows:
Creatures:
Nephalia Moondrakes
Mizzium Meddler
Daring Sleuth
Spells:
Haunted Cloak
Engulf the Shore
Turn to Frog
Supports:
Sphinx’s Tutelage
Tamiyo’s Journal
Choked Esuary
Ongoing Investigation
Lots of efficient cards and spells to keep my hand moving while keeping pressure on my opponent to keep up - while the spells are ready to provide contingency plans in case of something annoying showing up at inconvenient times. Engulf the Shore is the only mythic in the deck as I would prefer to not bounce my creatures in order to preserve my flow of cards being drawn/played.