Update: fixed the case between END and BEGIN markers.

1 while $text =~ s/(BEGIN_MARKER(?:(?!END_MARKER).)*?)a(.*?END_MARKER)
+/$1x$2/;
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This repeats the search and replace until it isn't found anymore. Not exactly "within one regex" but it is still pretty readable.

The part which reads (?:(?!END_MARKER).)*? will non-greedily accept any characters that aren't starting your end marker. It's a negative-lookahead inside a non-capturing group.