A agree with Jen,
That response does not look good. It looks like some more or less random tweaking rather than a systematic tune up. Satsagen is good but it is not giving you the phase information. The way I do it is to use a VNA and look at the Smith chart for alternating 180 degree phase shifts at the design frequency. That's by far the easiest way to do this.
However you don't have a VNA so the Dishal method is probably the best way. That involves detuning all the other resonators except the one you are trying to tune and then peaking that one. You can detune them by shorting them out, but in your typical tuning screw filter that's not easy, so once you have tuned it, simply de-tune it by a known amount, e.g. 1 turn clockwise, or more turns if needed and remember where it should be using pen and paper to take notes. Repeat for all the other resonators.
Once you have found the resonance of all the filters, then you can set them all back to where they ought to be. At that point, it will be close to on frequency.
You can't adjust the coupling in this way, best not touch the coupling screws if there are any. You are not moving it very far, so they should be OK already. Too late now I expect. If you have moved them, put them back using the high resolution photo you took before starting, or using other clues like evidence of exposure to air etc.
Edit - here is one I did earlier, it was originally somewhat below 70cm with I thing 6 resonators (might be 8, cant remember) that each consisted of a cavity with a disc on the end of a post tuned against the far end of the cavity (i.e. like a disc capacitor). I had to turn down the discs a bit to move it up in frequency. I then retuned it using alternating 180 degree phases in S21 (or S11 if you don't have S21). This was the result:

- filter_tuning_26463138126_o.jpg (103.05 KiB) Viewed 318 times
Not perfect, but good enough.
Mike