You're already going about prosecution very intelligently, so you're in good shape from the start. My advice for improving what you've got now is to simply assume that the target is evading at a right angle to the LOS at the time for firing for TMA purposes. This solution will represent the maximum bearing deviation the target can achieve, which means the target will be between that solution and the initial solution. Checking the current bearing will give you some more useful information and theoretically reduces your solution to two points, provided you have an evasion speed. As for opening vs. closing, you can check if signal strength is increasing by checking the # of narrowband lines or how clearly the lines are showing in DEMON.
Also, keep in mind it's much easier to get sphere/hull array contacts on an evading target than it was before he went evasive. You might be able to get some triangulation going, which will help a great deal with telling if he's opening or closing.
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