Sorry im in the middle of a move so responses are kinda slow.
The tune (.wrb) files you can save separately, and I'd recommend saving each one on its own before you flash so that if the newer file is bad you can flash the old one over.
Did Chris flash your ECU in the mail or do a remote tune?
Also its easier for me personally, to see if its the same issue as mine if you can take a picture of the graph logs like this.
View attachment 1670517
For me the stumbling happening matches with that red line right side where you see a kinda plateau in the AFR. If you go through the log like that you can see if there are any AFR spikes or dips at low throttle % that arent related to when you shift gears.
I can send you a PM of my fuel map later when I get the chance, might be tomorrow. I didn't use autotune because it seemed to do a wider