UK Residency Options

unless i'm reading something wrong, the original poster is just living with the family for free and is not paid for any household activities and has a full-time job outside of the home. 

This is exactly the case.
Right now, my two options are work visa/studen visa.

I have minimal dept, and I know there are several great engineering programs, so I may look into the education route as well.

Thats a very liberal interpretation of that quotation, and I disagree with it.

Nothing in that page, or indeed in the UKBA actual guidelines, says that the person must have been employed *full-time* with the employer.  The emphasis is placed on proving that this is a genuine relationship and has been in place for at least twelve months.

http://www.ukba.homeoffice.gov.uk/sitecontent/documents/policyandlaw/IDIs/idischapter5/section12/section12.pdf?view=Binary

A refusal can be issued on the grounds of length of previous employment.  There is no indication of a refusal being issued on the grounds of that previous employment not being full-time.

Given the dearth of this sort of situation on the forum, I expect it will have to remain a theoretical discussion.

But it does say that the supporting documents that are required include an original contract of employment and a letter from the employer stating the terms and conditions of the employment.  http://www.ukvisas.gov.uk/en/howtoapply/infs/inf17overseasdomesticworkers#Q9

It also says that if the employer leaves the UK permanently, the domestic worker is expected to go with them.  While it might not say so explicitly, this type of visa is clearly intended to be temporary and linked to a condition of employment that existed in the US.  So not what the OP is looking for, despite your pedantry.