No, you are not alone! I think Izzet spells is a far more difficult archetype to support than we give it credit for. It has this inherent weakness in that it needs a high density of both creatures and spells and the deck doesn't work without either.
My thoughts:
I tried
Saheeli, Sublime Artificier once, but I never actually did anything with it. I don't think I truly get the card, you must rely on that second ability for it to be worth the slot, IMHO.
Stormchaser's Talent,
Shark Typhoon. Both of these are good choices but you are right in that they are "cheating". They both slot in slower decks, not in the usual spellsingler deck. Stormchaser is weaker and mana-inefficient, but Shark Typhoon is solid enough that it opens up synergetic possibilities without forcing them. Note that both work well with
Replenish if you ever want to run it.
Monastery Mentor is interesting in that it's off-colour but it would be too strong if it weren't. That creates an interesting dynamic and, frankly, it's a top-tier design. Its cost forcing you to tap-out, the lack of haste and trample in the tokens, the geometric damage scaling...it's all a great puzzle. The fact that it's in white keeps it a secondary card in my cube, though.
Third Path Iconoclast. This is what you want Young Pyromancer to be, but it's a UR card so it isn't. Noncreature Pyromancer is what we are all looking for. It goes in and out in my cube. I feel I don't want both and, if push comes to shove, I'll choose the original.
Young Pyromancer is the face of the entire archetype for better or worse. When it works, it's great. When you don't have enough spells or when it gets blown up, it's a waste of cardboard. But it's one of those cards that do work, unlike Third Path Iconoclast, it can feed a BR sacrifice deck, for example.
Haven't played with either Toph or Fire Nation Occupation.
Geralf the Fleshwright feels like a storm win condition, the kind that aren't fully parasitic but still not that useful. Theorically, it can work with creatures, creature Gravecrawler loops or abuse Earthcraft but...I haven't actually used it that way. It seems more of a theorical possibility than a real one.
I think the biggest payoffs you haven't mentioned are the following:
Arcanist is valuable, not just because it's a powerful spell-based card but because it gives you additional triggers for your other creatures. After all, if you run, say, 12 spells, that's only 12 triggers for the entire game! Arcanist gives you more, which is extremely valuable.
Like Arcanist, this is good because it lets you increase that spell density you often lack. It's a cheap creature, too and becomes a 3/3 flyer which is big enough to be a threat with some support.
The original is too weak, but this version is just fun. I like it because it's a pure spells-matter card and with a wholly unique effect, too. It's big enough to justify supporting it. It creates mind games, since it can turn any creature into a 3/3, making it a good early blocker to stave aggro (a bad matchup for Spellslinger decks) or push damage against midrange. It's also great with tokens, which the archetype tends to have around.
it does nothing without you casting spells left and right. But it gives you a unique, powerful payoff for that.
Personally, I think the archetype is increasingly expressed through creatures that invite you to pile up spells but aren't actual "spells matter" cards:
