I am happy to report the solution.
I created a track of the screen, then on a separate layer, rotoscoped the obstructing object.
I turned OFF the tracking for the obstructing object's layer, and only exported the screen's layer, applied it in AE, and that's all for part one.
To get the screen to lie behind the obstructing layer, I did the next step:
I returned to Mocha, selected the obstructing layer, and now exported shape data.
Back in AE, I pasted that shape data onto a solid, and with the tracked footage underneath, used that shape as an Alpha Inverted Matte.
It worked!!
I also purchased the Curious Turtle Rock Steady course on AE CS5/Mocha v2. Hopefully that'll help further.
http://www.imagineersystems.com/store/index.php?target=products&product_id=...
Sources: Lynda.com's "AE CS5 New Creative Techniques: mocha tutorial" lesson
Creating Motion Graphics chapter on track mattes