I'd stick with the conventional approach here. All else is bound to be a dirty/bad hack. You don't like redo? Fine, you can use a nested loop.

local $_;

do {
    my $rec = '';
    do {
        $rec .= $_ = <>;
    } until /^Field 3/ or !defined;

    # ...

} while defined;
[download]

Makeshifts last the longest.