Safety neutral switch

It depends on how much current your push button can handle, and how large the wiring is from batter supply --through the button -- to the solenoid.

I am SURE that using the BM switch for a "full current" push button is NOT recommended, so you still need a relay of some sort.

Frankly, I see no need to get rid of the starter relay. If you want something heavier, you could use a starter solenoid like a Ford, but you'll need to get one wired so that the two small terminals are the coil connections. Very Few start solenoids are wired this way.

There was an oddball had 5 terminals used on AMC?? that would work, but they are a little rare

How 'bout the ignition bypass circuit? Are you running a ballast resistor type ignition? IF so, the newer Jeep start relay will handle that function, as it has a second contact.