I searched for quite a while for an answer to the same question but couldn't find any answers. I do have an idea, though:

(1) Save the form field values as cookies.

(2) Make your submit "button" a simple link to a script. Since it's a link, right-click to open in new window/tab will appear and work.

(3) Have that script grab the form values from the cookies.

Since there are no other solutions to this on the web that I can find, I should get a gazillion points for this answer.