You're right, of course.
But as you point out, in real-world calculations, these mass changes can be as safely ignored as the relativity-induced mass increase that results from moving my car from zero to sixty miles per hour. ;)
Off Topic » in reply to A bit more detail...
But as you point out, in real-world calculations, these mass changes can be as safely ignored as the relativity-induced mass increase that results from moving my car from zero to sixty miles per hour. ;)