While investigating on this issue regarding the failure of feeding filaments with my AMS HT, I realized that the direct connection with my X1C was in fact too direct.
The PTFE tube coming from the AMS HT was attached to a 4-in-1 PTFE tube adapter without the spring loaded buffer!
My regular AMS was instead connected to the spring loaded buffer and then to the 4-in-1 tube adapter, and actually it was working fine.
So the solution for me was to connect both my regular AMS and the AMS HT first to the 4-in-1 PTFE tube adapter that was then connected to the spring loaded filament buffer.
Then the output of the spring loaded filament buffer was attached to the X1C.
Now both AMSs feed the filament smoothly.
Hope this information could be helpful for you.