OK I got it working, too.
To help someone else, this is what I did:
changed (as noted elsewhere in the thread) the memory/time settings in the modbak.module.tpl
I did this:
// memory / time settings
$zip_time_limit = 480;
$zip_memory_limit = '20M';
$db_time_limit = 480;
$db_memory_limit = '20M';
I had a lot of trouble figuring out the path -- the module itself seemed to be looking in the public_html folder of my site, but I didn’t want the _backup folder there.
I ended up changing the default line in the module
$modx_backup_dir = $_SERVER['DOCUMENT_ROOT'].'/_backup/';
to one with the path hard-coded without the modx variables at all and enclosing the path with single quotation marks:
$modx_backup_dir = '/NameOfServer/MyUserNameAtTheHost/_backup/';
I should add that it only works for me without including the database tables.
To be sure I have it all covered, I also exported the database thru PHPMyAdmin.