The machine is supposed to start at the pressure shown in the "minimum pressure" value in the machine's settings. It should only go lower than that value if you hit the "Ramp" button. I can see where the pressure dropped to 6.0 when you hit the ramp.
If the pressure starts off at 9.5, the auto-adjusting action of the machine should not cause it to wander down to 4.0 at any time.
To say that in the reverse way, if the minimum pressure is 4.0 as shown in SleepyHead, the pressure should start off at 4.0 and not at 9.5.
Do you have a copy of EncoreBasic, the program that your DME uses to look at your machine information? It might be good to look at a daily report for your machine with that program.
Alternately, you could print out the three daily graphs from SleepyHead and show them to the respiratory therapist at your DME. Mention the three pressure values: starts at 9.5, ramp set at 6.0, but drops as low as 4.0 during the night.
Other stuff:
If you are awake a lot with the machine on, then yes, that will make your
AHI lower.
Your leak rate doesn't look high except for the period between 3:30-4:30. The top line on the leak rate graph is the total air leaving the CPAP-human system. It includes air that goes out your mask vent plus any air that leaks out your mouth or between your mask/nose.
There is an equation for the amount of air that's supposed to go out the mask vent depending on what the machine pressure is. I'm not clear on all the details, but the machine uses that to figure out the unintentional leak rate (the bottom number on the Leaks graph). The bottom number is the one you want to look at.
Your machine has some liters/min value for leaks that it considers to be too high. SleepyHead also has a value. I'm not clear if it gets that value from the machine or if it uses a default value. My SleepyHead program has 24 liters/min set as the threshold value for "Large Leak". You can see the value SH is using if you look under "File - Preferences - CPAP".
Sorry to hear that your chin strap was uncomfortable.