Ok Craig well I know we are speaking via phone which isn't a problem but for the sake of others I'm going to post here as well.

So looking at the pics and speaking to you i'm confident you have it wired correctly. So this will 99% just be a setup issue.
This could be 2 second fix and soooooooo simple you'll scream.!!Lol (Or 5min and you'll still scream)

I'm going to presume you have setup the Motor output pins and Input pins in Mach3 as per Cnc4you instructions.

This could be 2 things that are the same really.! Your E-stop should be NC switch type so this would mean the Input the Active state would be Low.
To Mach this means if NO voltage on that pin then E-stop machine ie E-stop active when pin voltage goes LOW(zero). You have NC switches so the circuit should complete voltage will flow and all be well provided you set the correct pins. (Check the E-stop isn't pressed. .Doh!!)
Now if Mach3 is in charge of the inputs then the thing that could stop Mach3 resetting is if the active Low setting is wrong. In this case it would be correct if showing the (x) meaning Active when Low. If it's ticked then this is your problem. 2 sec Fix.!!! . . . . . . . . .Now take a deep breath and try.! . . .Then scream.!!

But I think the UC300 plug-in could be in charge of inputs here and it's Active State is reversed (Active High) and when it see's Voltage it's saying to Mach E-stop.!
Easy way to tell is push the E-stop button and Mach should reset as the Uc300 pin will go LOW.
In which case you'll have to go into the Plug-in settings and change the Pin state to Active LOW.

So first quick test to see who's in charge of inputs mach or UC300 push e-stop and try resetting mach. If no joy then check the Active state of the E-stop pin in mach3 inputs. No matter which state, Ticked or unticked, toggle it to opposite and try reset again.

If none of these then we'll look deeper.!