I don't know how the factory fw works, but mine can put almost 100% power if the temperature doesn't match the setpoint even by 1°C, the pid integral will keep rising and rising, but only if the tip is able to transfer the heat.
Yes, stock fw hides the real temperature because it probably bounces more than a kid in a fun fair.
I've recently added a small filter (5°C) to remove these annoying constant little changes, but the real temp will be shown when the threshold is surpassed.
Give it a try, you have original backups to revert.
All I can say is T12 are a very random thing, some perform a lot better than others, even smallers doing better than bigger ones.
The main issue comes in the TC bonding with the tip.
If poorly bonded, it'll read the heater temperature, instead the tip body, I've had tips reading 300°C under water, while others did much better.
Also they calibration can vary a lot, more than 50°C.
New tips are often a bit unstable, after a while they start working nicely, and few months later they start losing thermal performance.
I'd get a beefier 150-200w 24V power supply and mod the station to use JBC.
Also, I've heard JBC overshoots on purpose when detecting load, so when you think you're soldering at 300°C, it's actually rising the temps to compensate, but I can't verify that.
My fw doesn't do that because I can't trust these T12 tips, they all behave different, so better stay in the safe side.
You have the boost option which increases the temperature for a specified time and returns to normal, so you'll hardly damage anything by forgetting.
Anyways, the temperature control is pretty good, I've used it a lot at 380-400 and even 450°C when using small tips to solder grounded pins, and very rarely damaged anything, only when applying excessive force and other screw-ups caused by me.
If you want Soldering Iron comparisons use this channel: https://www.youtube.com/c/Sdgelectronics
Edit: here is the playlist
https://www.youtube.com/watch?v=AMvZfOWkApw&list=PLZzwMlLVLdOBBz8pwjt9CJhEJFYVfHSH2
He should re-test the performance with the newer pid and filtering algorithms, I thing it'll do better now.