Eric,
Yes you can use FlashBuilder 4 with the SFV 1.3 as long as you do as you mentioned and use the 3.x SDK and the 1.3 AGS API. As far as where to drop the output, there seems to be a little confusion there on your side. What you need to do in Import the whole SFV 1.3 source files as a project into your FlashBuilder 4 development environment. Then as you build the project and debug it the compiled swfs will be in the bin-debug folder of your project and when you are happy with your development then you export a release build and then the compiled swfs are in your bin-release folder and are ready to be copied to your web server.