I would suggest using the commandlet Export-Mailbox, as you described. There is an article on the MS Exchange Team Blog that goes over its usage and discusses the permissions needed. (There is a newer post as well that is more clear)
Since I have found their post to be somewhat vague on setting the correct permissions, I prefer the instructions in an alternate post, which show how to give yourself permissions on all accounts or only on an individual account (my preferred method when I only have to export a few accounts). Basically, before running the export command, you run:
Add-MailboxPermission –Identitiy “MailAlias” –User Username –AccessRight FullAccess
where "MailAlias" is the account you are trying to export, and Username is your account (or the account you will be running mailbox-export as). After that, export away:
Export-Mailbox –Identity <mailboxUser> -PSTFolderPath <pathToSavePST>
Lastly, to be clean, I like to remove the permissions and return things their original state, so:
Remove-MailboxPermission –Identitiy “MailAlias” –User Username –AccessRight FullAccess
After that, you are all set, you can take those PST's over to your new server, and import them. (You will probably need to grant yourself FullAccess to the new mailbox in order to run the import)
As an aside, the reason you need to run the pst export on a 32-bit machine is that the export has a dependency on Outlook, which is currently only 32-bit (this is described in the second posting from the MS Exchange Blog). I recall somewhere that MS was planning on correcting this limitation with the release of Office 2010.
Best Answer
Check this out:
Importing and Exporting Mailbox data to and from PST files Exchange 2007