Is this approach reasonable or am I missing something?

You're making the mistaken assumption that consumer cameras, even those we call "pro-grade", intended for taking creative or documentary photographs are precise enough for what you are asking it to do. The EOS Rebel T5i is not a lab-grade instrument. Neither is the Canon EOS 1D X Mark II, the Nikon D5, the Sony α9, nor any other camera made for taking pictures rather than scientific measurement.

The shot to shot variation of your camera's precision with regard to exposure may well be larger than the frame to frame difference of your subject.

For more, please see the comments following this answer to Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?

Is this approach reasonable or am I missing something?

You're making the mistaken assumption that consumer cameras, even those we call "pro-grade", intended for taking creative or documentary photographs are precise enough for what you are asking it to do. The EOS Rebel T5i is not a lab-grade instrument. Neither is the Canon EOS 1D X Mark II, the Nikon D5, the Sony α9, nor any other camera made for taking pictures rather than scientific measurement.

The shot to shot variation of your camera's precision with regard to exposure may well be larger than the frame to frame difference of your subject. Tolerances that are totally acceptable for creative and documentary photography can be woefully inadequate for laboratory measurements.

For more, please see the comments following this answer to Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?

Also related:
manual mode in DSLR with constant iso, shutter speed and aperture, intensity of the image still changes, particularly this answer
Why can't ISO, shutter and aperture speeds be controlled more precisely rather than sticking to a fixed scale?