Well, I didn't use a noniterative method and I actually don't know how I could, but I now use a "binary search" for attack angles to get a precise MEA that doesn't take heading or velocity into account. I may make a page for it with diagrams, but for now you would just need to look at the code to see what I mean.
I modeled the problem as 2 intersecting circunferences (bot moving and bullet moving) and 1 intersecting line (wall). There are at most 2 points where the 3 intersect. Then repeating it for all 4 walls for 8 escape points. Add the 2 escape points from classic MEA (ignoring walls) for 10 escape points. Do some out of bounds checking on all points and then find which remaining 2 gives the widest MEA.
There are some loops but they are fixed and independent from bullet travel time. Making it very cheap to calculate.
I can post the algorithm later.