Is there a way to import forms created in the old JotForm format into this new JotForm Card format and keep the same form address?

Yes, you can do that, here is how:

1) Find the URL of the classic form: https://www.jotform.com/help/401-Where-to-Find-My-Form-URL

2) Click Create form:

3) Then choose Card form:

4) And click Import form:

And use the Form URL that you have.

Let us know if you have any further questions.

Thank you!

Just spoke to my colleague about the previous post. He asked me to follow up for him. 

If you would like to keep your form ID then cloning it wont help.

Instead you should switch your layout. You can do this in your form settings.

For example:

All Questions in One Page is the standard layout.

One Question in One Page is the Card form layout.