NO NO NO
Don't do it, it is possible you intuitively feel your back is not up to scratch.
My advice is focus more on back work for awhile especially bridging exercises.
Also, instead of squatting, work on calf raises with that poundage and above. You should be able to do calf raises with a bar on your back with far, far more weight than you can squat.
Perhaps also consider some partial squats in a box.
Make sure you have safety in place as well.
And possibly consider getting a checkup, perhaps a chiropractor, I found them to be excellent if you get a good one. I know one guy who had a neck that was on its way to fusing solid, the chiro detected and fixed it.
Remember that if you do in fact have some inherit back weakness, and you bully your way through it, and it goes wrong, it can be the end of you.
Possibly I am over-reacting, everyone feels a little fear when confronting their max squats, whether that is 100 pounds or 700 pounds.
I am just trying to be pragmatic here. Maybe it is only nervousness, but best to ensure everything else is OK.
Please note that if you are already on 300lbs squat then probably your back is not dodgy, but probably just a bit lagging.
Maybe if you posted your other lifts people might look at them and realise your back is lagging?