Chalk it up to a good life lesson on how a market works.
The market could care less what we all think or even how beautiful your car is ... we aren't buying your car.
Your car is only worth what someone else in the market is willing to pay.
I can assure you, if any of us (including you) were BUYERS, we wouldn't care what the seller thought the value of the car was, we would only pay the absolute minimum we could get away with ... we'd look at what other cars like it are selling for and try to get under that. None of us are going to say, "well I could buy one just like it for $3500, but you know what, you think its worth at least $5,000 so what the heck, I'll give you $5,000."
So if you want to talk about value (as in $ worth in the market), the accurate statement is, your car is only valued at $3500 if that is all anyone will offer. But remember, its those dastardly buyers like you and the rest of us that make it so.
Your raw math equation is as follows:
IS $3500 + $200/month maintenance savings >= losing BMW + Enduring Sales Process ... or in other words, is $3500 cash in your pocket plus a reduction in car expense worth more than giving up your BMW
There are some good ideas in the other comments, all saying the same thing - the more people that see your vehicle, the greater chance you have at finding someone who values your car more than $3500. Its just math.
But here is the good news. If you ever want to get back into a similar BMW, you will be able to buy one for $3500 - a huge value for you.
I do hope you get as much as possible for your beautiful BMW.