Is this the thing that can /should be done in a single golfed line? Alternatively, is there a module that I should be looking at?

Is this part of a larger project? Then, golf wouldn't make much sense.

A simple way, in addition to the solution already posted, would combine the keys into a search expression.

From your description, it isn't completely clear (for me) what you are trying to do. I'll give my alternative below:

 # ==> $keyptr, @inputs as in your code

 my $rg = join'|', map quotemeta, keys %$Keyptr;
 my @hits;
 push @hits, { /($rg):(.+?)(?=(?:$rg)|$)/g } for @inputs ;

 # thats it
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You could dump the result w/the following loop:

 ...
 for my $rec (@hits) {
    print "====\n";
    print "$_ => $rec->{$_}\n" for sort keys %$rec
 }
 ...
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This would print then:

 ====
 ANALYSIS =>  yada ^M yada 
 CONCLUSION =>  drone drone ^M 
 PREFACE =>  mumble ^M 
 REMARKS =>  ixnay
 ====
 ANALYSIS =>  Chuckle 
 DEFERRED =>  blahblah ^M blah ^M 
 NAME / NUMBER =>  John 369
 REMARKS =>  Yada2
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Regards

mwa