Fructosamine provides a gauge of how well BG is controlled. The value is based on what BG has been over a period of two to three weeks. If the cat is on too much insulin and chronically sitting at high BG levels as a result of the overdosing, then the fructosamine is bound to be high. Once a cat is regulated, the fructosamine test can possibly be used to determine if the cat is remaining well regulated but to use that as a tool to determine dosing is IMHO, incredibly dangerous. Unfortunately, most vets seem to think it's the holy grail. Now that you are home testing, use the numbers you collect to make dosing decisions for Big Boy. Your numbers are far more accurate.
I agree with everyone else. 3 units is a huge dose to start with and is likely causing the elevated numbers you are seeing. The insulin dose needs to be reduced and it is not safe for you to give insulin at a pre-shot reading of 84. I'd skip the shot tonight to avoid a hypo event.