Show branch name, not SHA, in statusline when comparing same file across different branches

[sjwo]

I am using vim-fugitive to view different versions of myfile from different branches: while viewing a given file in currentbranch, I give the command :Gvsplit otherbranch:%.

However, the FugitiveStatusline() still shows [Git(currentbranch)] in both windows, and myrepo/.git/<SHA>/myfile in the new window: this long statusline is harder to read, and does not show the essential information, which is the name of the branch, otherbranch, associated with this version of the file.

Instead, I would like to make the new window's statusline show [Git(otherbranch)] while still listing the file's path the same as in the first window: myrepo/myfile.

What would be the best way to go about making this customization?