@dogfishdesign – Although what your after is possible it is neither easy nor does it provide a good user experience. Maybe I am missing part of the bigger picture but conversion rates would be substantially better if you had one simple form and/or in your welcome email ask them to update their full profile.
If you still want to do it that way you will likely need to both create your own forms but also write the JS to submit the first via Ajax then trigger the second Popup. Triggering the Popups via JS is rather easy though so getting your forms working would be the hardest part..
Also if your going to go that route why not use a multistep form like gravity forms or similar and have only one Popup. If you custom make the form you could simply have both forms in one Popup and show/hide the correct form.
Hope that helps.