Does anyone know what my overstay letter should contain... detailed or brief?
Just need some good opinions. Such a headache getting things done right.
First, a 4 year illegal presence in the UK is not just a 'mistake' that can be easily explained or dealt with. You need a professional to assist you. I suggest contacting an OISC approved adviser that will have the knowledge and expertise to assist you properly. The vast majority of the people here are just lay persons who have been through the process and have learned a bit along the way.
We do not have the proper knowledge or experience for the situation that you have put yourself in. You need a professional.
As Garry said previously a lengthy apology for a 4 year 'mistake' would most likely just tick off the ECO that gets your case. Seriously, you need professional advice and assistance with your situation.
ETA: You need to read your refusal letter very carefully as well and check that they did not mention that you had tried to use deception to enter the country. If they did then you very well could have more problems then you realize. You also say you returned in October 2008 to the US ironically this was the extention date that overstayers had to be out of the country in order not to have a 10 year ban. Then you conveniently 'lose' your passport and get a replacement in less than a month and return to the UK in November 2008. This is precisely why American Women have a bad reputation with the immigration authority in the UK.