This is actually quite a wide-spread issue. I’ve had this happen on 4-5 different projects while migrating from dev to live in the past few months. It could be server-related, because when I dump and replace manually, I can run the migrate process in the new server normally (to run the replacements that wouldn’t work with find&replace).
There are no conflicts with plugins (tried disables) and there’s nothing visibly strange going on with wp_options.
The logs suggest a memory issue,
[fcgid:warn] mod_fcgid: stderr: PHP Fatal error: Allowed memory size of 268435456 bytes exhausted (tried to allocate 1601536 bytes) in .../plugins/wp-migrate-db/class/wpmdb-replace.php on line 283, referer: .../wp-admin/tools.php?page=wp-migrate-db&wpmdb-profile=1
Looks to me that there’s a process that eats up all available memory before crashing.