If you have developer resources you could look at using the Smartsheet API instead of third party integration service. Using the Smartsheet API you could add a new row to a sheet after the form submission is made. Note, requests to the Smartsheet API cannot be made directly from the browser on the form submission, but if you have a custom form built already you could have the form submission be sent back to your own server where the form is hosted from. Then you could write code that takes the form data and makes a request to the Smartsheet API from your server to add a new row to a sheet.

I'm having the same issue. Were you able to find a way to do this?