Sounds like there's air trapped and it's causing the temp to be higher. But of course this is based on speculation without seeing it. The way I got most of the air out when I replaced my radiator was to refill the coolant system with coolant, tighten the radiator cap and squeeze the top and bottom radiator hoses. This forces the air to find it's way to the spout where the radiator cap sits. Then remove the radiator cap, refill with coolant then cap it and repeat by squeezing the hoses. I did this a few times before there was no more air. Make sure to only do this when the coolant is cooled down, that way you won't risk getting burned.
Once you do this, make sure to fill the coolant reservoir halfway between the low and high marker lines. Then just warm up the car and see what happens. There may be some air left in the heater core, so crank your heat up and let the coolant circulate the heater core as well.
When coolant warms up it expands so if there's any air dislodged, it'll find it's way to the radiator cap spout and get pushed out to the reservoir. Then let the engine cool down completely and open up the radiator cap to see if any additional coolant needs to be added. Once you get it to a point where no more coolant needs to be added, any remaining trapped air will find it's way out through heat cycling. The system is designed to allow trapped air to find it's way out. But if there's too much air it'll take too long to purge.
Do that first and see if that corrects it. Make sure to use Nissan Blue coolant or equivalent.
As long as the autozone radiator that was installed is of the same spec/dimensions, then the overheating is unrelated to the radiator itself. I know that the 2nd gen FX/QX has two radiator models. A thinner core which was for the V6 (non-tow edition) and the thicker core which was for the V6 (tow edition) and V8.
A racing radiator will only help if you have some serious mods and race. Otherwise it won't do much in this case.
If you didn't have any temperature issues before the radiator failed then chances are the thermostat is doing its job. They tend to last a while and become inefficient over time. If the thermostat isn't doing it's job well, the fans will kick in. If you're over 95K miles and you still have the original thermostat, throw it on your to do list the next time you replace the coolant, that way you won't have to spend extra money on dumping coolant to replace it now.
Just as a precaution, check your engine oil dipstick and see if the oil looks like oil rather than coolant mixed with oil.
I have a feeling that bleeding the air out will fix your issue but if not, report back on your findings!
Cheers!
