Meursault, with this sort of puzzle where the possible values that the letters can take form a predefined set (as here or in a puzzle last year or so where the letters were the first 26 prime numbers), every letter solved reduces the pool of remaining numbers still out there. By the end there are very few possibilities left, so much of the effort is inevitably at the beginning.
I was actually quite relieved that there were only two bits of brute computation (solving for D, E, L and T, and then solving for M, I, K and O), both of which converged to single solutions very quickly. The rest of the solving was more or less linear (although I am sure there are alternative paths to the one I followed) and still involved a lot of careful calculation and checking.
With this sort of puzzle, I write everything down step by step and use an Excel spreadsheet for the calculations (it's tedious to set up all the clues as Excel formulae, but saves time in the long run). This doesn't stop going down blind alleys (as happened to me in the previous numerical puzzle last November), but makes it easier to spot the errors.