How about another way, which is memoization: at each position in the source code we never attempt to parse the same production more than once. This solves infinite looping as discussed by the author because the “loop” will be downgraded by the memoization to execute once. Of course I wouldn't literally use a while loop in code to represent the production. I would use a higher-level abstraction to indicate one-or-more or zero-or-more in the production; indeed I would represent productions as data not code.
This also has another benefit of work sharing. A production like `A B | C B` will ensure that in case parsing A or C consumes the same number of characters, the work to parse B will be shared, despite not literally factoring the production into `(A | C) B`.