I agree. Unless application fee is a tight access, I would say there is no harm in applying to any programs. How about UPenn CAMB? You might have already looked into it but I heard that they also take a lot of international students. Not sure if they have faculty research that would align your interest though. Worth looking nonetheless.
I can't tell for sure if a gap year will 'significantly' improve your chance. It will depend on your work and publication quality you get. As far as I know, students usually take 2 gap years but that is just based on people I know so I could be wrong. I believe it can definitely improve your resume. Based on my experience, most of my application deadlines are on Dec 1st/2nd and I got all interview invitations no later than Jan 15th. So you can apply to the programs in your senior year fall semester and if you are unsatisfied with your interview invites, then you can still apply to tech position in Feb? This is solely based on my experience so other people can chime in on this. But as I've mentioned before, you do have a good stat and seems to have great research experience so you do have a good shot at this! Good luck!