of course that will not work. the safety circuits are redundant. this means that everything is on two channels (Ch.A and Ch.B), and each button must break both channels. Since you have more than one button, you can daisy chain them but they still must have contacts on both channels.
An example would be something like this:
the way you drew it, each button would break just one channel. this not good because if the difference between channels exist (one broken and one not) safety controller would fault and also enter lockout state. typically, lockout state is only cleared by cycling power.
Ah, that makes perfect sense. I gave this a shot and it worked just fine. Thank you panic mode!