"I assume your goal is for each E-Stop switch to kill power to all motors and signal the Mach 3 controller."   Yes

"can you run dual contacts on each estop switch?"  I do not know the answer to this

"my arms are not long enough to fix this issue...."   That's just too funny!!   

"is this something you bought" Originally yes. The board in the black box failed and I obtained a G540 to control the motors. Gutted the black box and wired the G540 through the silver box.  (Necessity is the mother of invention. Dumb luck covers the rest)

"what kind of breakout board motion controller do you have and what is the black box" -  none - black box powers the spindle which is manually speed controlled via the dial on the box.  See attached photo

"Manufacturer and model"  Chinese SXCNC

think the easiest way would be to Change the e-stop button of the silver box to one witch has two NC contacts. eleminate the e-stop button
of the black box and put These two wires via a cable to the second contact of the e-stop button of the silver box.

Do you mean doing something like this??  (I am not sure so i am asking)

It appears you are showing a separate switch from the ones mounted on the boxes and are planning to replace both with this new one. That should work.

This leaves the problem of wiring the two E-Stops to the Mach 3. If each box has a contact for as the E-Stop output they can be wired in series as discussed earlier.
If not show us what you have. 

"show us what you have"

1st one (black box) is a lay37(pbc) estop switch

Two switching circuits: 1 Normally Open + 1 Normally Closed (DPST: Double-Pole-Single-Throw)
Contact rating: 600V / 10A
Number of terminals: 4

seen here:  https://www.aliexpress.com/item/4000135749528.html?src=google&src=google&albch=shopping&acnt=494-037-6276&isdl=y&slnk=&plac=&mtctp=&albbt=Google_7_shopping&aff_platform=google&aff_short_key=UneMJZVf&&albagn=888888&albcp=1582410664&albag=59754279756&trgt=539263010115&crea=en4000135749528&netw=u&device=c&albpg=539263010115&albpd=en4000135749528&gclid=EAIaIQobChMIgdvJodu26AIVCo7ICh1k0AOTEAQYASABEgIHX_D_BwE&gclsrc=aw.ds




2nd one (silver box) is a Shisnao SAY7 -  PBC Y090 LAY 37

LAY37-10ZS NO:normal open;LAY37-01ZS NC:normal close 

Two switching circuits: 1 Normally Open + 1 Normally Closed (DPST: Double-Pole-Single-Throw)
Contact rating: 600V / 10A
Number of terminals: 4

seen here:  https://www.aliexpress.com/item/32819686974.html?src=google&src=google&albch=shopping&acnt=494-037-6276&isdl=y&slnk=&plac=&mtctp=&albbt=Google_7_shopping&aff_platform=google&aff_short_key=UneMJZVf&&albagn=888888&albcp=9594035441&albag=102695258807&trgt=296904913880&crea=en32819686974&netw=u&device=c&albpg=296904913880&albpd=en32819686974&gclid=EAIaIQobChMIpInindy26AIVlJOzCh0bQwVREAQYBCABEgLEq_D_BwE&gclsrc=aw.ds

Thanks everyone. I was way over thinking this.  I removed the black one and rewired through the silver one.

Next...   adding X, Y and Z limit switches.

Novice.