I have a verbal offer from an off cycle job that interviewed over the summer, which was my first interview and first offer. It's a great academic fit, but is in a location that my partner is not happy about moving to, for family reasons. I have until early fall to decide (yes, that's a long time, there are circumstances I'm not going into for anonymity). I'm still applying for jobs in our city and nearer areas, particularly one dream job that just opened up, but I worry that even if one of these jobs is interested in me, they won't get back to me until too late, because everyone else is on the standard fall/winter cycle.
My question is, is there any way to politely tell these other locations that if they are interested, they need to let me know ASAP? These are places where I have either just turned in an application, or I am just about to turn in an application, so this would have to be in a cover letter or unsolicited e-mail. I don't want to hurt my chances by coming off as egotistical or strange or trying to rush things before they've even decided if they want to interview me, but on the other hand I have promised my partner I will do absolutely anything I can to stay where we are. It will be hugely stressful for our relationship if we have to decide on Offer A when we haven't yet heard from Dream Job B. So is this a thing that people do, or would this look like a weird red flag?