Complete replacement is neither necessary nor possible. At the usual atmospheric pressure, quick loss of consciousness commonly occurs when concentration of oxygen in the breathed gas mixture is between 0% and 6%.
The feeling of suffocation occurs at elevated CO2 levels. If the OP just exhales into the ambient atmosphere (obviously, you can't breathe out back into the canister with pressurized gas), then there is no any significant CO2 buildup, unless breathing happens at a reduced rate, that shouldn't be the case according to the statement "my breathing regularity is normal".
It's surely possible to pass out from inhaling nitrogen through the month from a latex balloon, and this should be possible with breathing in from a tube connected to a canister with pressurized nitrogen as well.
Of course there's going to be some trace amounts of oxygen and other atmospheric gases in the bag, I didn't mean literal 100% replacement 0.0000000000000000000000% oxygen.
If we want to get extremely technical, we can go with 'near-complete' replacement of oxygen. That's how this method works, by replacing the oxygen in the exit bag with inert gas and pushing any exhaled CO out the bottom while simultaneously preventing oxygen from coming in the opening.
And yes, I've already described in my post that suffocation is caused by carbon dioxide. It's clear OP is inhaling oxygen in some way and producing carbon dioxide. The only logical conclusion is they are inhaling it from their surrounding environment. It's very difficult to pass out from inhaling an inert gas from a balloon, the most you are going to get is lightheaded.
The cylinder lists "Carbon Dioxide less than 1ppm, H/Cs (as CH4), less than 1ppm, Oxygen less than 2ppm, Moisture less than 2ppm". They've tried this on two separate tanks as well. Don't think this can be the cylinder composition in any way.