Do you really want the "most powerful" or is staying under a certain pricepoint your goal? The HH Magnum is probably the most powerful brushed motor of its size (that being 540/550) but it's definitely not cheap (seeing how you scoffed at $80) at $150. It uses neodymium magnets and a 775 sized rotor along with many other features that make it not only more powerful, but smoother than most 540/550 brushed motors as well.
As far as 3 slot vs 5 slot goes, all else being equal, the 3 slot will produce more torque and more peak wattage, it just won't be quite as smooth. For your criteria, I'd suggest staying with a 3 slot. The same is true of lower turn count (faster) vs higher turn count (slower) motors, the lower turn count will produce more torque and more peak wattage, at the cost of power efficiency (lower run time from a given battery), but you must make sure you gear correctly so you don't burn it up. You'll be much better off running a very fast motor with very slow gearing than you would be running a slower motor with faster gearing.
Then you need to consider size. A 550 will always make more torque and more peak power than a 540 of equal build. If your car can fit the extra length of a 550 (generally +/- ~6mm longer than a 540), always opt for the longer can (unless the tiny bit of weight gained is more important to you than the power gained.)
At the throw away pricepoint, a 3 slot, 12t 550 like what comes in a Traxxas Slash/Rustler/Stampede (yes, that's pretty fast in a crawler) geared waaaaay down might be the best fit. HH makes a better variation of that motor in their Trailmaster Sport line. $20ish.
Moving up from there gets you into the machine wound rebuildables like HH and Team Brood offer, as far as I know, Tekin does not offer a 550. Around $50.
Next step up would be a hand wound from the same sources. Around $100.
Then you've got the Magnum at $150.
Ready for the ringer that'll ruffle a few feathers around here? Check out the $50 Surpass Hobby 540PLUS motors. They pretty much snaked all the ideas that went into a Magnum motor and used whatever cost cutting measures they could to reach a pricepoint. Now, I'm not saying it would be equal to a HH Magnum, nor am I saying it's junk, but if it could perform say 75% as well, that should still put it WELL ahead of anything that's even close to its $50 price.
Do you also need a new esc? If so, I'd suggest going with something that can run 4s. It does not sound like ultimate low speed resolution is on your list of criteria, so something like a Hobbywing WP880 could fit the bill for ~$30. It's Programmable (same program card as the wp1080, only the 880 only has a 6v bec... but even that is 4a) If I'm honest, it isn't quite as smooth as the 1080, but still a good bang for the buck in a scenario like yours.
