As an alternative to @SteveV's strategy, there is another way to approach this puzzle, by considering:
Using this method, it is possible to use even smaller odd numbers than in that answer, right across the board:
Note that it is impossible to use this same technique to find a solution requiring the removal of just one letter...
The answer is that William had clues
To start with, here's what we can initially determine about the numbers for each clue:
Klaus Teuber game played around LA
Alpha (Feigenbaum's specifically; no need to make this puzzle harder than it already is)
886.., er, I can’t remember the last 2 digits