It was no fun quitting the game to switch to DX9, but I knew it'd be necessary after stumbling upon this unpleasant information. I went about minimizing my headache like this (after the typical slow-computer tuning like stopping unnecessary services, live antivirus scanning, closing all system tray icons, cleaning up in MSCONFIG and rebooting, etc).
I changed my default audio device within the control panel to use 16-bit 44khz souund (assuming it's not already that low or lower). This helps reduce some of the processing effort involved in the sound system. I had enabled exclusive access as well and the game is very good at giving it up to the OS and switching back and forth to whatever default sound device you pick.
Make sure you have the latest NVIDIA driver from NVIDIA directly, and remove any stereoscopic / 3D stuff from your "Programs and Features" control panel after the install (or before if you can) unless you're really into that sort of thing; I don't know if it literally saps the driver in any way as some claim, even when you're not using the effects, but it's something that people like to get rid of right away :)
Your video driver (in my case "NVIDIA Control Panel") may let you do certain things like drop the max color depth to 16 bit, which is probably worth doing right away on a slower machine to give it a huge relief, and I don't think your Windows desktop setting for color depth will ever determine what the game uses and don't think the game has an [exposed by UI] setting.
You'll be annoyed by repeating the mission but can prepare and bring 1-2 Saints along with the mission NPCs (Shaundi and Pierce). You won't lose respect if the regular Saints croak but you need to keep the NPCs alive so the extra Saints can provide some cannon fodder and suppressive fire. The police Peacemaker is a good car to have for this, 4-passengers and quick.
Be armed to the teeth if you can (I brought the sniper rifle to help me keep away from the flame thrower brute while dealing punishment), and lower your resolution within the game as far as you can without losing any of the picture due to cropping on your display. In my case, the second-lowest resolution (1100x600, something bizarre like that) worked but the lowest of the low (700x400 weird numbers, not 720x480) cropped out much of the picture around the edges.
I got to the hanging shootout before the elevator scene, was sure to spend a lot of time keeping my assault rifle loaded while picking off the enemies (this part had become child's play from my head-banging attempts previously), and then I switched to the cropped weird otherwise unplayable resolution right before the brute cut scene began, and I was able to see more of the scene (though it still seemed to be missing stuff) and had enough opportunity playing the game at this higher speed to unload a bunch of shots into his face and chest (with the higher-end assault rifle), and fortunately succeeded to knock him off on the first try. It seemed surreal and impossible, because I had wasted so much time trying to figure it out...
For context, I bought a cheap Athlon XII 645 3.1GHz HP desktop around 18 months ago and really wanted to play SR3 when the recent Humble Bundle was released. It was intolerable with the "NVIDIA HD Graphics" internal card, so I flailed around in whored mode trying to have some fun since the story mode was too tedious and had flashbacks to playing Street Fighter II the PC Game at horrible speeds on my 286/12 with 1MB of RAM when it insisted on a 386 with 2MB in order to function. This time I had the luxury of spending a minimal sum to resolve the issue...
I added a basic $30 eVGA NVIDIA 8400GS video card with 1GB of DDR3 RAM because I wanted enough oomph to play the game, but not with the weight of a major investment since I'd recently picked up an Xbox 360 with Kinect and didn't want to go nuts buying a new power supply and cooling system and the whole slippery slope after going gangbusters on a crazy video card. I just really wanted to enjoy this title from the PC perspective (and get an HDMI out!) as a former Wolf3D, Catacomb Abyss, Heretic, ROTT, Doom, and Quake junkie, for a low price.
So this was a few nights ago for me, and I've fallen in love with playing the game for unhealthy durations with a 32" TV right in front of me, with decent headphones.
But I wanted a faster experience, and after some initial hassles I got Boot Camp working on my MacBook Pro i7 2.2Ghz with an internal NVIDIA GeForce GT-650m. The game is insanely faster and there's a huge noticeable increase in your ability to whoop ass, drive like a maniac, etc; you have extra frames to play the game, rather than sluggishly flailing away. Sounds obvious but the difference felt amazing after trudging through slowly. I think this MacBook is the fastest machine I've used personally so far, and Windows 7 (64bit) seems to scream a lot faster than Mac OS X (Mountain Lion), probably in large part because the Windows OS by default won't use the internal low-end Intel chipset when display needs are minimal, and instead uses the NVIDIA chipset exclusively. But in any event, it flies, with Aero running and everything...which I also disable on a lower end machine when gaming :)