Thank you Dark_Knight19 for posting your solution! I was struggling with solving this non-recusively for hours, and your post inspired me to try a recursive solution.

I ended up coming up with this solution:

if(head1 == nullptr && head2 == nullptr)
{
    return nullptr;
}
if(head1 == nullptr && head2 != nullptr)
{
    return head2;
}
if(head1 != nullptr && head2 == nullptr)
{
    return head1;
}

if(head1->data < head2->data)
{
    SinglyLinkedListNode * temp = head1->next;
    head1->next = mergeLists(temp, head2);
    return head1;

}
else
{
    SinglyLinkedListNode * temp = head2->next;
    head2->next = mergeLists(temp, head1);
    return head2;
}