Upvote:6
The UK border is very tough.
I can't give you a yes/no answer, but since you have already overstayed one visa, it would be perfectly reasonable of them to assume you are going to overstay a second one. If they think this they won't let you in. You'll be officially declined entry, it will be entered in your passport, and then good luck travelling anywhere outside of the USA on that passport.
Basically I wouldn't risk it. I've been held in an interrogation room at the UK border for a situation similar to yours. Not fun. I hadn't overstayed any visa but I was relying on older agreements between New Zealand and European states that pre-date Schengen, are still in effect, but not widely known about or understood.