I do not understand the question, you mean that this (removing the repeat-while loop) does not work for you?

# repeat {  # Replace class with inline styles (repeatedly)
$new ~~ s/  class \= \" (\w+) \" / style="%classes{ $0.Str }" /;
#  } while $new ~~ /  class \= \" (\w+) \" /;
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Or do you mean you want to make it work for multi class stuff like: <span class="foo bar">lorem</span>