Just one of your code lines to comment:

print @filehandles[$i] if (/@regex[$i]/../^END_OF_BLOCK/);
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First, at the very least, to refer to elements of an array, this should be:

print $filehandles[$i] if (/$regex[$i]/../^END_OF_BLOCK/);
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Second, I do not really see the point of the ../^END_OF_BLOCK/ part in your context.

Finally, I cannot test right now, but I don't think that:

print $filehandles[$i] $_;
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is going to work properly. I think you probably need something like this:

print {$filehandles[$i]} $_;
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Otherwise, some of the errors that you have would be picked up by the compiler if you had used the following pragmas:

use strict;
use warnings;
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at or near the top of your script file.