Your beam never launched off the first mirror correctly which can be seen clearly by burn 4 and 5. Probably made up for some of this with mirror 2 which is why burn 1 2 and 3 were good.
If you get close to spot on you will see similar…fine most places but not at say far corners.
Why it improved after moving the tube is simple. You changed the launch angle of the beam into mirror one and without intending to may have improved its subsequent launch off mirror one.
Reflecting a laser beam off of mirrors is like playing the game of pool. Angle in equals angle out accept in pool we bounce the cue ball off the bumpers in a flat plane. The lasers bounces off its mirrors in all 3 axis and so complicated the process.
In more complex laser delivery systems like medical CO2 lasers we spend a lot of time making sure launch angle ism perfect before every going to the delivery mirrors which are the ones that move…for us it is mirrors 2 and 3. In medical CO2 we have 6 of them in an articulating arm…yep 6…its fun to align. If our equivalent of launch off of mirror one is even slightly off…you will never get rid of beam walk. I would spend a lot of time getting this perfect.
It is tougher on our cheap chinese lasers as we do not have a combined red laser beam back at the tube or this whole process would be exponentially easier as we could see the red beam move real time instead of doing burns.
Back on track though when you moved the tube you also changed the angle in and angle out of mirror 1 which showed as an improved or changed result out at I assume mirror 3 burn. Which shows the launch out of mirror 1 was off.
When I check to see if mirror 1 is spot on I want to have the beam travel as far as possible so I tape a large craft stick over mirror 3…yes 3. I then run X to its max position away. Now i will move Y to 0 which is close to mirror 1…do a burn. Then run Y to its limit and do another burn and check it. Since I did not move X then mirror 2 is not affecting beam coincidence…IE burning in the same spot. Even if 2 is off it will only affect where it burned but if X never moves then it should burn in same spot.
I do it this way as the final check for mirror one as it gives me the farthest travel of the beam to spot movement.
Just taping the burn stick in front of mirror 2 only gives me a 1/3 of the beam travel I can get by using mirror 3 and X at max distance.
In preliminary mirror 1 adjustment then yes I tape burn stick over mirror 2 thats just to get it close first.
SO here mirror one is the launch mirror and everything needs to be perfect or it just gets worse as distance in x or Y is increased