My question now is this: Since during the profiling process the R/G/B and brightness values of the monitor are changed, I cannot simply switch profiles in Windows' color management, can I? If this is true, I would have to calibrate it every time I want to switch between the two. There must be a better way for this, right?

The process consists of two steps. First you set the display as close as possible to the desired state and then you measure it and create the profile. So the profile is describing the state of the display from the first step. If you change the display settings, the profile becomes incorrect.

Now, I could just turn off any alteration of the monitor's values during profiling. Is this the way to go? Are there drawbacks to this method?

Depending on the calibration software you have, you could, for example, leave the monitor at 6500K and 160cd/m2 and make the calibration for 5000K and 100cd/m2. In this case the corrections will be written to the profile and applied by the software to the image data. Since the data have limited precision and fineness (max 256 levels for 8bit video), they are sensitive to modifications and you are increasing your chance to get posterization, uneven gradients or some other undesired artifacts. I'd suggest getting the display hardware as close to the desired settings as possible.

Possibly the software you use would allow you to create the profiles with manual control over the brightness, contrast and RGB settings. You could write down what the setting was when you were prompted to change it during the first calibration step and change it manually when you switch between the profiles.

My suggestion would be to use just one profile and one setting. Unless this is really good display designed for color critical work, my personal preference would be around 6500K (closer to the native white point of the display, 120cd/m2 or so and native gamma.