Close.... Here's what I would do:

1) Launch FCP
2) Close any open projects (not even an Untitled project should be open)
3) Go to Final Cut Pro>Easy Setup
4) Choose the Easy Setup that matches the format you recorded the majority of your footage. I normally shoot in XDCAM EX 1080p 30 VBR (VBR = HQ and CBR = SQ)
5) Import media (your recently converted .mov's)
6) IMPORTANT: Go to Final Cut Pro>User Preferences - Render Control tab and change the Render Codec to: Apple Pro Res 422 [HDV,XDCAM HD/EX/HD422 only]

So in summary, what you've done here is set up a project where all new sequences will be created with the XDCAM EX codec, but anytime you RENDER, the render file will be ProRes codec (which yields better results than rendering in XDCAM EX). Buy doing this, you can drop your clips into the timeline and they will play without rendering (assuming your hardware is fast enough....which it normally is).

Hope that helps! :)