I am pretty sure Strange Horizons isn't saying "if you query on day 71+, your query will be ignored and you will be shot on sight". I think what they are saying is to ignore the general submission rule of thumb which involves waiting a month or more extra after a magazine's stated "will respond within" date and actually query them as soon as you can if you pass that date.
I am assuming you received an autoresponse to your submission, so you shouldn't have a problem and will most likely receive a response within the 70 days (I haven't had a non-response from Strange Horizons yet).
Also, I don't know anything about the Chizine contest, but I definitely don't think I would email Strange Horizons to tell them I needed them to respond real quick so I could send my piece elsewhere by a certain deadline if they rejected me. That is sort of like asking to be rejected. If you miss the Chizine deadline, so be it. They always have a regular slushpile to go through if you really feel your piece is perfect for them. And new contests/anthologies/etc come and go constantly.
I know it can be frustrating watching that clock tick by and knowing that other clocks are ticking by just as fast, opportunities passing, but patience is a must in the submission process. An annoying, mind-boggling, head-banging must.
-Michelle