The first half of your plan sucks...no other way to say it.
You'll have no home or job in the US -- basically nothing to go back to, I don't think you'll be allowed entry because you don't meet the requirements.
This page explains what documents you should have when coming to the United Kingdom as a general visitor.
They are:
■if you are employed, a letter from your employer granting leave of absence from your job for a specified period - the letter should also say how long you have been employed by that employer, in what job(s), and when you are expected back at work;
■if you are self-employed, evidence of your business activities and financial standing;
■evidence of any property you own in your home country;
■if you are a student, a letter from your school or college stating the course you are on, its start and finish dates, and the dates of the holiday period when you intend to visit the United Kingdom;
■evidence of any family or social ties and responsibilities to return to;
■evidence of any firm travel plans you have made;
■bank statements going back over a period of several months; and
■evidence of savings available to you.
You're an unemployed, homeless, American Female...3 strikes already, I seriously doubt that they'd let you in to begin with.
Add to that you're going to intentionally lie to an Immigration Officer to gain entry by saying you're only going to stay for 2 months and then change your ticket after you get in and stay for 6 months -- bad idea they can check to see when you left and using deception to gain entry (whether successful or not) can be used to refuse any future visa applications you make (even spouse visas) under Immigration Law section 320(11).
Considering that you have never met in person, I'd keep it to a short trip (2 weeks maximum) and have an alternative plan just in case things don't work the way you hope that they do...have enough money to fund your entire trip without relying on someone else so you will have hotel/hostel, food, transportation, sightseeing just to name a few big ones.
In theory, yes you can visit for a period of time, return to the US together, get married and apply for your spouse visa. But, dont lie to the IO, have plenty of funds for the trip, get health coverage (travel insurance) to cover you for the entire length of your trip as you cannot use the NHS, and have a plan B in case things don't work and you realise they're an axe murderer or something.