I think it would be extremely difficult to "prove" you weren't going 50, or even 30, for that matter. About all you can do is offer "testimony". Whether or not the judge "believes" that testimony is another issue. Your "friends" are usually presumed to be biased toward you. The finder of fact decides credibility.
Island County is the ONLY county (although there may, indeed, be others) I've heard of that charges an administrative fee PLUS the original fine. Here in Kent, you only pay an admin fee (I think it's still around $150). Then if you receive ANOTHER ticket during your deferral period, they impose the original fine, as well.
Personally, I'd still ask for a contested hearing and submit a discovery request. There are so many little things, such as not filing the ticket within a week, if the officer doesn't write that the radar was in "proper working condition" at the time, etc. that can get the ticket dismissed. But, you won't know unless you receive the discovery materials.
You can always change your plea to "mitigation" and send in your request for a deferral AFTER you view the materials.
But, the decision is ultimately up to you,
Barry

