"Maye the balance could be to not display Marks convictions until specifically asked for?"

This is basically the status quo before. But ... the employer is going to background check mark and find them anyway, because they are public record and available in easily searchable databases (see Lexis, etc)

In practice, this stuff simply doesn't affect any employment case (at least in the US). None of the right to be forgotten stuff allows you to avoid any of the above except the "easy google search" (which again, practically doesn't matter).

So the argument you make should be limited to that. (and i think it is entirely reasonable to question whether your neighbors, who won't background check you, but will search google, should find it)