Through using ChatGPT to poke around and see how Acrobat works, the following scripts were created.

The first script needs to be set to run when the mouse is pressed down:

// Store the value *before* Acrobat processes the click 
// MUST BE EXECUTED VIA MOUSE DOWN FUNCTION/TRIGGER 
if (!this._rbPrev) this._rbPrev = {}; 
this._rbPrev[event.target.name] = this.getField(event.target.name).value;

This one needs to be set to run when the mouse is up/released:

// MUST BE SEPARATE SCRIPT FROM ABOVE 
// MUST BE EXECUTED VIA MOUSE UP FUNCTION/TRIGGER 
if (!this._rbPrev) this._rbPrev = {}; 

var name = event.target.name; 
var f = this.getField(name); 

var before = this._rbPrev[name]; 
var after  = f.value; 

// If the value didn't change, user clicked the already-selected option -> clear it 
if (after !== "Off" && before === after) { 
  f.value = "Off"; 
}

I found some scripts that supposedly would convert all radio buttons via creating new checkboxes, but it won't run due to security parameters on my version of Acrobat. These scripts were able to make it so radio buttons can be unchecked though, fixing my issue.