JDMase, yeah I hear you on the extension cord daisy chaining, I wouldn't do it with lights but with fans its very low wattage, I have done it in all my grow rooms. Like I say just never with lights.
As for extraction, do you not have a chimney breast in the room? Even if its go no vents in it will of had somewhere. In my room I took out the old vent and made it bigger to put the extraction into, then I have an 8" hole in the chimney at the other side of the breast which goes all the way to the basement, I was going to use an intake fan but its passive at the moe and works well.
Anyhow maybe this isn't possible in the house you have.
Just to point out too, a filter on the floor as said will pull hot air down but it will also pull air in from the easiest place which is the open tent doors or vents at the lower part of the tent. So essentially most of your heat is rising and staying there building up.
Get that fan and filter moved sunshine, an extension cord is really just a long wire divided by a plug with pins to connect the electricity, as long as your not pumping 600w through it theres no reason for it to overheat at all. We are talking about one fan.
The only other option if the girls are getting stressed is less wattage in light. Plants would probably produce better with less wattage if they are happy than with more wattage and stressed constantly.
Good luck with it, fingers crossed you get them temps down.
Edit, JD I just reread your earlier posts, I confused where you said plants were stressed in veg and not so much in flower tent. If temps high point is 82.4f (28C) your not doing to bad.
It used to be folks would say 78-82 was optimum(20years ago) now I see folk having a panic at 82degrees, not sure why. Anyhow, it may not be perfect but should be fine. Still get that fan and filter raised though ey.