I'm going to take a guess at what you're after - feel free to ask me to adjust the markup if this isn't what you tried to describe.

I cannot seem to get the button to cover both columns due to it being constrained within the slds-size_1-of-2 parent div

The key to this is to get the button out of that parent div with the 1-of-2 class on it and into its own div which will take up 100% of the parent container (the form) width.

<aura:component implements="flexipage:availableForAllPageTypes" access="global" >
    
    <lightning:recordEditForm recordId="0036A000001eZcVQAU"
                              objectApiName="Contact">
        <!-- the messages component is for error messages -->
        <lightning:messages />
        
        <!-- fields in the left column -->
        <div class="slds-size_1-of-2">
            <lightning:inputField fieldName="FirstName" />
            <lightning:inputField fieldName="LastName" />
            <lightning:inputField fieldName="Email" />
        </div>
        
        <!-- button in its own div in the center of the lightning:recordEditForm container -->
        <div class="slds-align_absolute-center slds-m-top_medium">
            <lightning:button variant="brand" type="submit" name="save" label="Save" />
        </div>
    </lightning:recordEditForm>


</aura:component>

Which renders like this:

I'm going to take a guess at what you're after - feel free to ask me to adjust the markup if this isn't what you tried to describe.

I cannot seem to get the button to cover both columns due to it being constrained within the slds-size_1-of-2 parent div

The key to this is to get the button out of that parent div with the 1-of-2 class on it and into its own div which will take up 100% of the parent container (the form) width.

<aura:component implements="flexipage:availableForAllPageTypes" access="global" >
    
    <lightning:recordEditForm recordId="0036A000001eZcVQAU"
                              objectApiName="Contact">
        <!-- the messages component is for error messages -->
        <lightning:messages />
        
        <!-- fields in the left column -->
        <div class="slds-size_1-of-2">
            <lightning:inputField fieldName="FirstName" />
            <lightning:inputField fieldName="LastName" />
            <lightning:inputField fieldName="Email" />
        </div>
        
        <!-- button in its own div in the center of the lightning:recordEditForm container -->
        <div class="slds-align_absolute-center slds-m-top_medium">
            <lightning:button variant="brand" type="submit" name="save" label="Save" />
        </div>
    </lightning:recordEditForm>


</aura:component>

Which renders like this:

Additionally if "cover both columns" means you want a button that stretches the full width of the container you can add the slds-button_stretch class to the button markup.

<div class="slds-align_absolute-center slds-m-top_medium">
    <lightning:button class="slds-button_stretch" variant="brand" type="submit" name="save" label="Save" />
</div>