Lower order pyramid elements was a warning not an error. How far did the solution progress?
I also ran Quadratic Tet elements, and got the solution to the point where the Highly Distorted Element error stopped the solution. Is that the error that stopped your solution? That is why I switched to Linear elements. Did the quadratic elements allow the solution to go to higher or lower time (pressure)?
The correction is to create better element shapes that do not get so distorted. In the linear mesh shown below, the pressure reached 0.08 MPa without any problems. I suppressed the other chambers to get the solution to run faster. In this solution, I suppressed the contact with the chamber wall-to-wall. You can unsuppress that when you solve since you can see some interference beginning.
Here is the Force Convergence plot. I broke the pressure into 2 steps. The reason is to save solution time by taking larger steps in step 1 and smaller steps in step 2. Note that step 1 should have ended at 0.05 MPa instead of 0.032 MPa because the convergence was still easily converging up to that point. Change the pressure at Step 1 to 0.05 MPa before you solve and it may give you fewer increments.
If I had changed the Restart Controls as shown below, I could have added Step 3 to increase a load and start the solution from the end of step 2. By default, the setting for Retain Files After Full Solve is set to No and so at the end of the solution, you can't restart from the end, you have to solve from the beginning.