Provide option to pay PayPal or Cheque

Our dilemma, hit the submit button, it goes straight to Paypal. What if they don't want to use PayPal? What if they want to call our office and pay directly by phone and still submit the form online.

You can make the Payment integration not required, I checked your form and I can see that you've already done that, and when I submitted your form, I was only redirected to PayPal if one of the products is selected. 

If you want to give your users the option to pay directly, you manually add your products using form fields, and then providing an option to pay via PayPal or pay at the office, if PayPal is selected, then the value is passed to PayPal and then you'll be redirected, if pay at the office is selected, then they're just shown the normal Thank you page. 

Here's an article that you might find useful, as it will explain how to pass a user defined value to your payment field:

How-to-Pass-a-Calculation-to-a-Payment-Field