The only way to tell rsync to apply different treatment to different files based on their name is via filters. Filters can determine whether a file is synchronized at all, or whether a file is deleted, but they can't determine the method used to check whether a file is up-to-date.
So you'll have to use two separate rsync commands: one that excludes this file and one for this file specifically with a different file comparison method.
rsync -axvq --exclude /home/my/some/filename.xx … / email@example.com:/backup &&
rsync -axvq --checksum --include / --include /filename.xx --exclude '*' /home/my/some/ firstname.lastname@example.org:/backup/home/my/some/
In the second command, I synchronize the directory but exclude every file in it except for the file to transfer. The reason I do that is to copy the directory's timestamp, which would otherwise be modified if
filename.xx is created. If this edge case doesn't bother you, you can simplify the second line to just copy