I have replicated this problem on our production server at Glenfield College. The white screen is generated when apache experiences a SIGSEGV fault, which causes it to create a core dump and terminate.
The cause of the crash is the php script running out of memory, and in our case it was set to the default of 128MB in the php ini file. After we adjusted this figure to 256MB the upgrade proceeded smoothly after that.
Personally I suspect it was simply the sheer size of the database, and other factors, that consumed the memory during the upgrade process. Now, I know this won't help those of you with hosts that have a strict memory limit on the PHP script you are allowed to run, but you could have a go at running the update on a local machine and uploading the results to the host [after doing your backups, of course].