We have a custom internal exporter that relies on code bits that aren't more widely available, so it's unfortunately not really portable.
There are rumblings internally of trying to do some improvements to the exporter, but given the problem here -- which amounts to resource issues that will naturally vary from host to host -- I don't know that there's really a silver bullet. In other words, any changes we contribute would maybe make the exporter more easily extended but not necessarily more useful on shared hosting for large sites, since you'd still run into resource issues. In those cases, a mysqldump is generally cleaner anyway.
Another option, by the way, would be to export by date range and do smaller chunks, though I believe this can leave file attachments behind (something we do hope to work on eventually). Since you'll be able to copy your file directory over, that may be a lesser concern, however.