Time complexity of looking up in a rainbow table
If we count a single application of a reduction function as 0.5 calculation [...]


That does not seem to be an assumption made in the paper? I would expect the reduction function to take much less time than a hash/cipher, so discounting them completely is a good enough approximation. That gives the value in the paper.

If you count it as 0.5, then it would take $0.5 + 2 + 3.5 +\dots + (t-1+0.5t)$ rather than what you have, since at each step you add 1.5 work for both another hash/cipher and another reduction.


  In contrast, the original method seems to call for $t(t-\frac{1}{2})$ calculations, fewer than the author's $t^2$.


This part I am not sure about. I would think it should be $t(t-1)$, which matches the later text saying that a rainbow table approach takes half the time of the original.