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D_Alex comments on Satisficers want to become maximisers - Less Wrong
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Here is a (contrived) situation where a satisficer would need to rewrite.
Sally the Satisficer gets invited to participate on a game show. The game starts with a coin toss. If she loses the coin toss, she gets 8 paperclips. If she wins, she gets invited to the Showcase Showdown where she will first be offered a prize of 9 paperclips. If she turns down this first showcase, she is offered the second showcase of 10 paper clips (fans of The Price is Right know the second showcase is always better).
When she first steps on stage she considers whether she should switch to maximizer mode or stick with her satisficer strategy. As a satisficer, she knows that if she wins the coin toss she won't be able to refuse the 9 paperclip prize since it satisfies her target expected utility of 9. So her expected utility as a satisficer is (1/2) * 8 + (1/2) * 9 = 8.5. If she won the flip as a maximizer, she would clearly pass on the first showcase and receive the second showcase of 10 paperclips. Thus her expected utility as a maximizer is (1/2) * 8 + (1/2) * 10 = 9. Switching to maximizer mode meets her target while remaining a satisficer does not, so she rewrites herself to be a maximizer.
Cool example! But your argument relies on certain vagueness in the definitions of "satisficer" and "maximiser", that between:
(These definitions are from the OP).
Looking at the situation you presented: "A" would recognise the situation as having an expected utility as 9, and be content with it (until she loses the coin toss...). "B" would not distinguish between the utility of 9 and the utility of 10. Neither agent would see a need to self-modify.
Your argument treats Sally as (seeing itself) morphing from "A" before the coin toss to "B" after - this, IMO, invalidates your example.