The selected process model must have a SAIL start form

You can apply this check to the interface itself instead of a process model. And instead of a loop, you can just end the process. Because the process is configured to have a start form, you should land back on the same interface. 

Try chaining the process from the starting node to the forms, this way the site can display the task on load

The main disconnect here, in case it wasn't clear, is that you can't define a process model as a Site Page unless it has a start form.

In your case, I'd suggest just using an interface for that site page, and allow the user to click a Start Process Link to begin the process model, in which case you can perform the checking in the initial XOR gateway and route them to the correct task. You will need to enable chaining and correct the flow directionality from between the upper task node and the XOR, before it will work correctly.