Upvote:0
In the end, I went to apply for a US visa without extending my UK visa. I applied in London. It went well. There were two stages: 1. document checking 2. interview. The two stages were done with two different people. In the first stage, the fact that my UK visa will expire soon after was actually written down on my documents by the staff (i.e., a message intended for the interviewer). But when I attended the interview, this issue was not brought up.
Upvote:1
The six-month rule applies, as stated, to passports. It does not apply to your visa. The point is for you to have a place to go when you leave the US; they don't necessarily care whether it's the place that you consider to be your residence.
The possible effect of your impending visa expiration is more subtle: it may make it more difficult for you to overcome the statutory presumption of immigrant intent. That is, it tends to weaken your case that you plan to go live somewhere else after the end of your trip.
Still, there's no absolute rule that prohibits a visa from being granted in your circumstances, so there's every possibility that the visa will be granted.