So none of the ejecting methods worked because the files are indeed in use, i.e. locked and the OS does not allow you to eject the volume. This is the line from the console showing that:
The operation couldn’t be completed. (OSStatus error -47.)" (fBsyErr: File is busy (delete))
The open files seem to be the following:
com.apple 762 mf txt REG 1,8 32768 639477 /Users/mf/Library/Mail/V2/MailData/Envelope Index-shm
com.apple 762 mf 6u REG 1,8 206848000 639476 /Users/mf/Library/Mail/V2/MailData/Envelope Index
com.apple 762 mf 7u REG 1,8 1676872 639478 /Users/mf/Library/Mail/V2/MailData/Envelope Index-wal
com.apple 762 mf 8u REG 1,8 32768 639477 /Users/mf/Library/Mail/V2/MailData/Envelope Index-shm
com.apple 1389 mf cwd DIR 1,1 374 436438 /Users/mf/Library/Containers/com.apple.MailServiceAgent/Data
The strange is that it says it is com.apple which locks them. But there are also two process IDs shown, then 762 and the 1389, so pls run the following command:
ps -ef | grep 762 and ps -ef | grep 1389
This will list the process details for each process ID.
BTW on my mac, once I quit mail, at first the lsof for Mail showed
MacBookAir:~ macme$ lsof | grep Mail
SystemUIS 8925 macme txt REG 1,2 380069 3233963 /Applications/Mail.app/Contents/Resources/document.icns
mdworker 27337 macme 4r REG 1,2 15364 6063211 /Users/macme/Library/Mail/V2/.DS_Store
mdworker 27339 macme txt REG 1,2 21488 7166495 /System/Library/Spotlight/Mail.mdimporter/Contents/MacOS/Mail
but soon after the last two lines went away as the mdworker (spotlight) finished it's job, so in my case I would be able to eject.
Rgds
Zsolt