So far as I know, anydvd can be run with any program. It just runs in the background and does its thing separate from the burning and or compression application. I do know that it works fine together with at least some programs that also have copy protection removal functions. Its free to try it out though, so there’s really nothing to loose (you don’t really have to pay even to use it to trouble shoot your problems as long as you find a solution before the free trail runs out). Personally I think its the best copy protection program you can get.
As far as a strong reader, The strongest readers I have are not made anymore (I have a half dozen good drives so I have not had any reason to get any of the current models available). The last new drive I got was a pull from a dead system that someone abandoned (didn’t need another drive but a free liteon for scanning was nice). Perhaps someone else could make a suggestion on a strong reader from whats available right now though.
Also, you could look at the more popular drives right now in this poll.
then go to the specific brand forum here
and read the review to see if its a strong reader (a lot of the reviews are stickied at the top of the forum for each brands forum).
This one looks like it has potential
Note, I do not have this drive so I am only pointing it out as a possibility (I have an 18x samsung that is a decent reader, not my best reader but pretty good). Maybe someone that owns it can comment.