I am sorry to hear that your site traffic has dropped. That is never good news for any webmaster. Hopefully you will be able to recover soon enough though!
When you said that you dropped about 5 weeks after the initial email, how much did you drop? Percentage of G referrals? Were your G referrals steady up until that point?
I don't want to stir the pot, but I'm curious if maybe you got hit by one of the algo updates over that period of time. Possibly the bad/unnatural links that were giving you value were really just devalued? The second one I really wonder about because so many of the big blog networks took a hit over the past month or so. If these links were giving you value, losing them would demote your overall sites authority. This could in turn have an affect across the board.
It just seems so crazy that they could demote your site because they have decided YOU purchased the links. How does Google truly know that you have bought links until you actually admit to it? Up until that point it seems like it could be anyone placing the links, especially competitors if they know it will have a negative effect.
I have heard that some people affected have been able to see improvement by continuing to focus on building better quality links. Not sure if that's an option, but definitely something to consider.