Standardize the benefits of an advantage: Talents and Reputations would give +1 die each. Specials of any stripe would either give +3 dice each, or +1 die and open up a possibility like a power. So a gadget could give +3 dice, or open up new narrative possibilities such as "rocket powered jetpack". The distinction is "can an unskilled person do this?". If it's something anyone can attempt, but you're just really good at it, the special gives +3 dice. If it's something normal people just couldn't attempt then it lets you do so, but only gives +1 die. Mysticism would be broken out into separate advantages so you'll get a larger advantage specializing in just one or two powers than grabbing them all for the bonus dice. You could still take multiple levels in a single "power", with the first level giving you the power +1 die, and subsequent levels being +3 dice each. Romantic Interest gives +3 dice to your rolls (only) if the Interest is an NPC. It gives +1 die to each players rolls if the Interest is a PC. Action Example: Fighting Styles would add +3 dice, but Piloting would be +1 die and the ability to fly and land airplanes, autogyros, and airships (which certainly opens up new narrative avenues). So if you wanted to be a really good pilot, you'd take two levels of Piloting for the ability to fly all sorts of aircraft and a total of +4 dice on piloting rolls. You could conceivably come up with a special fighting style that gives a power and +1 die, such as martial art that gives the ability to run across the surface of still water.
Companions as a second (minor) PC: As per the rules, each PC can have a maximum of one companion. The companion is a second minor character you get to build. They have Styles of 3/2/1(0) as in the main rules, but you actually make them a character sheet with advantages. The get a maximum of 1 rank in one special of their highest Style, and are otherwise mundane. They cannot themselves take further Companions. Your Companion can be active in other scenes where your main PC is not present, and if so you play them, and they have their own pool of Peril. Be advised that they'll frequently end up over their heads and need rescuing by a proper PC. If your Companion and your main PC are in the same location or scene, then you combine their Peril and make rolls only for your main character. In such situations, the Companion counts as a normal (+1 die) advantage that applies to all your rolls in the three Styles they have. (As an optional rule, giving all Companions Styles of 3/2/1/1 and +1 to all your main character rolls when present probably wouldn't break anything.)
Divy up the Style wedges: We change the style ratings and access to specials based on the number of players. With one player, we use the normal 5/4/3/2 rules from the main game, with Specials available in your best two areas. With two players, we'd do the same, but strongly encourage them to not overlap strengths or weaknesses. With three or four players, we scale back to 5/3/2/2, still allowing specials on your best two Styles (even though one is rated at a "3"), but reducing the points available within it, so there's a more pronounced gap between your primary and secondary specialties. Again we strongly encourage the PCs to not overlap their primary Style (so just one PC gets a "5" in Science, for example). With five or more players, we stick with 5/3/2/2, but now only make specials available for your primary style. In general, the larger the group, the narrower the PCs should be so that you don't end up with characters that specialize in the exact same things.
One calamity = one Peril: This is a clarification stemming from last night's play experience with a very large group. Let's say the whole party is on an airplane, and someone narrates that it's on fire and going down. That does not mean the entire group each get a Peril. Sure, they're all in trouble, but any one of them can solve the entire dilemma with a single good die roll. If there's one PC that seems more endangered than the others, the GM gives them the Peril. If all things are equal, the GM gives the Peril to the PC who proposed the danger, to reward them for enhancing the drama. If this danger came about because of GM narration, you give the Peril to whoever hasn't had one in a while.
Mysticism clarification: Several of the example Mysticism powers seem like a poor fit for the stealth-and-detective theme of the Mystery style. This is okay, you just use their bonus dice on rolling whatever other Style makes sense. It works in the same way that a Jet Pack bought with Science could add to an action roll. So, if you have Mysticism: Invisibility, you'd roll it with Mystery to sneak without being noticed, but you'd roll it with Action to make a sneak attack. Clearly, in the main game rules (where Mysticism gave +3 dice and the power but Fighting Style gave just +2 dice) that was broken. But given the house rules above, it would be in balance. Yes, you could spend two (out of 5 maximum) Mystery points in Invisibility to get +4 dice on all your Action attacks. If you'd instead spent 2 points of Action towards a fighting style, you'd get +6 dice on those attacks. That's still not perfectly balanced, but it's much closer and probably not worth quibbling over.
Optional Rule if +3 seems too good: From my limited experience with the system, I think the game is at its best when the GM is cruel. The pace should be unrelenting, with something bad happening every time the GM gets narrative power (which they do constantly). Peril. Peril. Peril. Nothing ever goes right for the PCs unless they're spending a success from a die roll. Given that pacing, having all Specials give +3 dice (or +1 and a power) is the right call. PCs get a few really big dice pools, allowing them some narrative breathing room when their specialties come in to play. But some GMs just aren't comfortable constantly beating the players down. If you think you're going to be nice to your players, you might compensate for it by dropping the bonus for a special down to +2 dice, and maybe even having specials taken to gain a power give only the power (no automatic die to go with it). If you're not planning to beat and torture the PCs at every opportunity, then there's no need for them to have such large dice pools. Personally, I think the +3 dice and unrelenting pacing would work better to make it feel cinematic and help differentiate between PCs, but some folks might feel that's over-the-top. I can't argue that it's not, I merely argue that I think over-the-top catches the spirit of the game a little better. Alternately, you could keep the +3 per level, but limit how many points can be put into Specials. Say, no more than 2 or 3 points of specials per Style.