I don't think you have to hide the numbers for what you are doing, but rather just how you get them.
I've made my game more player facing, i.e. they players roll all of the dice. But I've also made it more narratively driven, i.e. the players don't invoke their powers, instead, they describe their actions. (Taken liberally from *World games)
I did this in response to exactly the problem that you're having- that DFRPG can be overwhelming at times. So how does this work?
The first part about the GM not rolling takes a lot off of the GM's shoulders, and makes things faster. You then use this savings to spend the time to interpret the players' actions, and trigger them based on the narrative for the players that are less familiar with the rules. Rotes help a lot with this.
So, the only things you have to explain to your player are- the rotes that you help them design with their characters, and the meaning of overcasting vs standard casting. Once you've done that, the player describes what they are doing, i.e. casting their rote, or putting more effort into it or really pushing themselves. You look at the numbers behind the scene, and give them the target. They roll... and describe what they are doing to invoke their aspects as needed, since they know what they need to make the roll.
This way, they are eased into the aspects of the game that have to do with Fate, while the crunchy things of magical manipulation are kept behind the scenes.
In summary, let them describe it in the narrative, you do the heavy lifting, then let them roll against a static number, invoking aspects as needed to make the roll if they want to so with more narration.
1. Get a cheatsheet into each player's hands.
You know that godsend player, the one who always has the notecards? Key thing there: the notecards.
You've spoken to the group, and they got upset, but you know they cared enough to get the books in the first place. It's entirely possible that they do just forget, or maybe they're having a difficult time with the rules and don't know how to articulate it. Even if they read cover to cover (and maybe they already have), there's a lot of information to parse and remember, especially for new players. Even veterans forget rules sometimes! Still, fumbling through the book for basic rules is not time-effective. My solution is to create a cheatsheet. This has helped me as both GM and player.
Figure out your most commonly used rules. Type up these rules and print a copy for each player. Try to condense them as much as you can. Strip them to their bare bones so players can find the information they need at a glance. Also, since you'll be distributing the same page to everyone, concentrate on rules that everyone uses. I'll discuss character-specific rules later on.
It's just more practical for you to make the cheatsheet. If they don't have the rules down yet, they probably don't know which ones are the most important. You likely have a better grasp, and you're also the one who wants more efficiency. The best way to ensure that this happens is to do it yourself, and then the whole group will be on the same page.
For character-specific rules, though, it's best if the players do it. This spreads the effort around. Plus, you can use this as an opportunity to help re-familiarize your players with their mechanics. Sit down with them and help them make index cards or type notes from the book. Point out nifty features and answer any questions.
Assure them that it will make their lives way easier, because it will. They probably don't like book-fumbling either. They'll also be more likely to use their character's features if they're always right in front of them in an easily-digestible format. It's hard to achieve your full potential if you don't know where to find it. The key thing is to emphasize how useful it will be for them (in character and out) if they do this, not how much worse things will be if they don't. Make it about them and their potential fun, not your frustration, to avoid further souring.
It's awesome that the Battlemaster Fighter took the initiative, though. If this is something he enjoys doing, you could enlist his help! I'm this player in my own groups, even when I'm not GMing. I love having a cheat sheet, so if I'm making one anyway, why not share? At the least, use his notes as an example (if he's okay with it).
2. Make use of existing resources.
Cheatsheets you make will be the best-tailored to your needs. That doesn't mean you shouldn't use ready-made tools on top of that. People often share their own tools if they think they're especially useful. If you need something specific, search the web to see if it already exists. There's no guarantee that what you find will be useful -- again, you know your own needs best -- but it never hurts to try. If you hit gold, that's time and effort saved.
For instance, here are some form-fillable initiative cards that provide a quick reference of initiative order and PC skills, traits, and actions; here is a larger, longer version of a similar concept. Here's a site that generates spell cards. ENworld has many sheets available. It only took me a few minutes to locate them by searching "5e spell cards," "5e initiative cards," and "5e character sheets," respectively. You'll be more successful if you already know what you need, but you can still try searches like "5e game resources" and "5e player print outs" if you're looking for tools in general.
Your local games store is usually your best bet. Since a certain company encouraged game stores to provide in-store gaming space back in the early 90s they've become the center of the gaming hobby in many places.
Also, the social networking "Meetup" sites seem to be populated with gaming groups inviting people in.
If you are in the Long Island, NY area you are welcome to join in any of the games I run (Currently Call of Cthulhu, Delta Green and Dresden Files).
Good luck in your search.