I think you should hang on to that $400 until you've spent more time with what you have. If you are willing to get in and tweak the profiles, you can get a colorchecker arbitrarily close to published values with nothing more than free software. Whether this will actually be useful in practice with real-world images and workflow is debatable. But if you're like me you'll find it an interesting and educational process.
I spend a few minutes with you RAW file in the Adobe DNG profile Editor and was able to get all the patches within less than Delta-E 2 of published RGB numbers for the color checker. The profile alone can do this without touching a single slider in ACR (other than making sure your white balance is right, which, based on the 4th grey patch of your raw, I set to Temp: 4250, Tint: +26).
The most important part of the profile if you are going for numerical accuracy in my experience is getting the tone curve right. The default is almost always too contrasty and a linear leaves the shadows too dark. Once you get the tone curve right, many of the other colors fall in line. Depending on the character of your camera and light, you may need to push a few of the patches around a bit.
Personally, I don't think there's anything wrong with using hot lights and a cooling filter. The spectrum from that combination is going to be pretty decent especially when you have tools like ACR and DNG profiles at you disposal.
I've attached the processed raw, a diagonal cut comparison with published numbers—not perfect, but pretty good for a minimal effort, and the DNG profile I made/used.