Scratch all that.
No one's used A123 LiFes in like, 10 years. Those were the old 1st gen Dewalt lithium cells. A123's goal was to build EV batteries, but back then there were no EVs, so their way to establish an income source and business beachhead was to build tool batteries. They went out of business... I dunno, 8 years ago? Shopped around, was a ghost company for a while, and eventually someone picked up the pieces and tried to salvage the brands. They make new stuff now, but, no one uses LiFes anymore except in automotive starter battery replacements (and other RV and marine use that has always been based on the "12v" battery building block). And the only reason they're used there, is because they're so much worse than ordinary lithiums, and have lower voltage and energy capacity, that they coincidentally are a closer voltage match to lead acids if you chain 4 of them in series. With your other lithium chemistries, it's a awkward place between using 3 or 4. 3 is too low (12-12.6v is their ceiling, can't handle 13.8 or 14.4v that an alternator will put out), and will get overcharged. 4 is too high (16-16.8v full, 12v dead empty), and you're wasting half your capacity by never charging up fully.
LiFes are marginally safer (ltihiums went through a moderately bad phase 6 or 7 years ago as they'd found ways to get more energy into them but with less stability),
LiFes were originally used in power applications because the competing lithium technologies back then were unsuited for high power draw. As in, an 18650 would max out around maybe 2 amps. Today they'll do 50 amps. 1-2 amps was fine for laptops, right back to the 1990s, because you'd never drain a battery faster than in about an hour anyway. But it couldn't run so much as a dremel. Dewalt used them for 2-3 years before pulling the plug and switching to modern lithium chemistries. Woe on you if you bought Dewalt back then, they're not compatible with batteries before or after, basically just threw your money away.
LiFes are also really temperature and charge sensitive. The first time you try to charge it when the temp is below the freezing point, instantly ruins them, done, throw it away.
What I would use in your place is part of a used hybrid battery. Hybrid batteries are garbage for energy storage, but, nothing has higher power capacity than them, because they're designed to be fully charged or discharged in under a minute. The whole point is to recover energy while stopping, and boost your power while accelerating, without taking up much space.
A crappy old Prius pack will be ~200v, but, the cells are just stacked together like Lego bricks, you use as many as you want. You want a 50v pack? Use 1/4 of the stack. It'll be 20lbs. You won't pay anything close to $500 for one. Even 2nd gen Prius packs are rated for 36hp for the whole pack, so, using 1/4 pack, you'll be at 9hp, pretty close to your target.
Newer hybrids will have lithium packs that will be a fraction of the size and weight, and, usually aren't overly desireable. You can probably buy portions of a pack on ebay.
Or, if you can handle a minimal amount of DIY (a little soldering and making an enclosure), something like this: 48v 6.4ah 307.84wh Battery with Panasonic Cells - $81/kWh
$25. 48v. Pack will easily push 100A, has a 150A fuse if you push it. That's 5hp. Put two in parallel if you want, you're at 10hp. For $50. They're "used" but were premium grade medical backup packs and most of the time, literally never discharged even once.
I don't know what methodology led to you picking a specific voltage, but you could find or make or modify packs to be any voltage you want. Generally, if you want a motor to spin faster, you need a higher voltage (or, to choose a motor that was physically designed to spin faster at a lower voltage).
You could skip that, use a DC motor (nearly free) and handle the speed by belts or whatnot. Same way you would have to if it was engine-driven. If your goal was to get away with as low of cost as possible, a 10HP DC motor, or, one capable of 10hp in a surge is probably $20-40 in scrap, and they're thrown away all night and day.
Generally controllers can handle higher voltages and just choose to chop it down to whatever voltage the motor wants. So you don't necessarily have to match your battery voltage to your motor voltage. Higher voltage being better if possible, because you have the option of higher speed (lots of amps at low voltage will end up sitting idle because it can't push the motor faster than "max" for that voltage).
I didn't even know they made motors for BLDCs that didn't have hall-effect sensors. Yeah, you can spin them up blindly because they're low mass and can get yoinked into the position that matches the coil pulsing, but, I didn't know anyone did that.
Also, they're going to be... fragile. The little motors are skimpy and lack thermal mass. So, their "max" power is not really a suggestion like it is with the heavier iron. They're built like a balloon, not like a bridge.
7500 watts out of an RC motor is... a lot. Like, a lot a lot. It should be the size of a volleyball, but, it'll end up being not much bigger than your fist. Part of that corner cutting is that it'll be designed to be kept in massive amounts of airflow for cooling (i.e. at the axle of a propeller, free cooling), which, you won't have.
Stupid question, but why go electric at all?
Why not just power it off of the engine?
At the end of the day, the compressor is something you have to buy, and all you're saving going electric is having a way to spin it.
Did you want to be waiting years for this?
High power controllers have more or less bottomed out. Batteries don't have much more room to fall. And, there aren't any 10hp EVs floating around, you're off by an order of magnitude minimum, so, the costs of motor controllers dropping from the EV industry aren't going to exist from your perspective.
If you enjoy the process and want to spend time instead of money, you could get this done for really cheap. Junkyard and used parts, and then you spend your time and effort mashing it together. Any budget-conscious DIY project is just a series of bodges until it kinda works.