Hard to say what minute volume the quoted RR "means," and how that corresponds to an SpO2 given unknown pulmonary function. So it'd be nice to know, although admittedly partly for pathophys funsies. (Ever feel like you're performing an assessment just for the case presentation later?)
With no attempt to apply it to the actual patient, there ARE some BLS techniques for really maxing out the breathing patient's oxygen supply. If you're using a non-rebreather in the back of your wahmbulance, and that's what you're committed to using, remember that you can supercharge it by running up the flow rate past 15. Just keep turning the valve until it stops; usually this is, oh, well over 40LPM, and the excess flow helps get a spontaneously breathing patient as close to 100% FiO2 as you're likely to get. Sounds like a rocket ship, and don't try it on a portable tank, of course.
You could also try (and this is better if they're not moving a whole lot of volume) a cannula at relatively high flow -- perhaps 15LPM. It's not real comfortable, but if they're obtunded it's no big deal over a short period, and it does a better job of getting oxygen INTO their pharynx if they're not sucking it in very ambitiously (a mask just lets it overflow; a cannula shoots it into their airway under pressure). You can combine cannula and mask as well if you have two regulators.
Finally, if there's obviously gobs of oxygen getting into the lungs, yet their SpO2 remains low (and you believe it), the problem may be V/Q mismatch (shunt) -- O2's inside the lungs but it's not crossing the membrane to enter the blood. PEEP may be helpful, and in principle you can create it
using a plain BVM. But this probably wouldn't be very bright for the described patient, who is having hemodynamic troubles as well. (I will remain agnostic here on whether this somewhat sketchy technique is ever a good idea.)
You can also sit 'em up somewhat, although this is subject to hemodynamic limitations as well.
The only thing I'll say about the patient in the scenario is that sepsis is near the very top of the life-threatening emergencies we can help fix, and should be managed with appropriate vigor.