I am completely baffled by this one..
You state that you are overdrawn, even on a salary of £50k+, and then you state your wife has savings in excess of $75000...
At the risk of stating the blindingly obvious, why on earth didnt you immediately transfer money from your wife's account in to yours?? ( I am assuming of course that your account isn't overdrawn by £46k!!)
After all, as the British sponsor, they are looking at your ability to manage your finances sensibly and support two people on your income. It seems that you had a ready-made solution staring you right in the face.
You could even have channelled the money back to your wife at a few hundred a month via Western Union or bank transfer and built a paper trail of seemingly supporting her. It is difficult for them to say you cant support your wife in the UK if you have already been doing it since you met.
I earn around the same amount and have zero savings...£50k a year is a comfortable and respectable salary, so you must have some serious money problems. I supported my wife, paid everything here, and I travelled to be with my other half five times over six months, on that same salary.
(The latter shows the ECO not only committment but a very good disposable income.Two birds with one stone!)
As an added "boost" to my account when we decided to get married, I sold my car and sold a heap of junk on Ebay, and suffered public transport for 6 months. Being with my beloved takes priority over everything!
Now I can go shopping for a new car on top of all the excitement of my wife joining me. Life is grand. I hope you get things sorted.