stealing _dump was my first hunch too, but is that is called on (sub)values, it will be very hard to catch the *total* size. And you will have to force using Dumpperl (a.o.t. using the much faster Dumpxs).

{   my $size = 0;
    my $org_dump = \&Data::Dumper::_dump;
    sub Data::Dumper::_dump
    {
        $size >= 4000 and return "";
        my $s = $org_dump->(@_);
        $size += length $s;
        return $s;
        }
    }
[download]

could be a crude start ...

Maxdepth does not really help as I want the initial 4K to be correct (with no omissions) as far as it goes. _dump sounds interesting and I will look at it.