Both those sentences should begin with “As much as” rather than “Much as”. Exchanging the noun and pronoun has no tangible effect on the grammar or meaning of the two sentences.
Much as is quite frequently used as illustrated in those two sentences, but my understanding of the case is that such use is misuse. The only time when much as should appear in proper English not preceded by so or as or similar adverb is when it's being used as part of a simile. Two examples are shown below. In both of them, much as can be replaced by just as or like with little effect on meaning.
She stretched, much as a cat would stretch.
Much as an eagle would do, he soared out of sight on his wings of thought.
By contrast, in the question's examples, a statement of extent is needed (to tell how much Jason needed the money), rather than a simile; hence “as much as” is appropriate and bare “much as” is not.