My screen has been replaced and my phone is working again!
You might be onto something with the design of the torx bits. In any case, I went to The Source and picked up a set that included a T4, T5, and T6... heck, it was a set of about 40 different small screwdrivers and cost me 20 bucks, but I decided I didn't want to spend the time searching for smaller sets at lessor cost and bit the bullet.
Turned out that the T4 removed the 4 screws effortlessly. (note: the T6 removed the 2 black screws at the top)
Based on numerous posts/links that I've seen related to the proper torx screwdrivers for the Nokia E71, I recommend getting your hands on a T4, T5, and T6 and then it will vary as to which one will work best for you. It's dependent on the screws and as Gorgonesh stated it could be the design tolerances of the torx bits as well.
When you're removing the screws, it should be immediately clear that they are unscrewing. If not, then stop and use a different screwdriver else risk stripping the screws. They should rise up and unscrew right away when using the proper sized screwdriver whether that be a T4 or a T5. (T6 for the 2 black screws).