Add to that the relatively high quiescent current of the AMS1117 regulator. 9.34 mA sounds about right.
I am using a HT7133 which is much more low-power than the AMS1117.
Oh, right. I missed that.
Then its 20 mA min - 30 mA typ. max output current seems on the low side though. A 1200HC will typically draw 18.8 mA during programming (see datasheet).
It also has a
peak start-up current that may exceed your regulator's capability. The datasheet suggests to use Diamond's power calculator to estimate it. I just checked on one of my designs (with a 7000HE) and it gives 68 mA for VCC and 15 mA for VCCIO!
(Additionally, if you targeted such low power, you should have chosen the 1200ZE instead...)
The highish average current you're measuring may indicate that the MachXO2 is caught in an endless start-up loop (desperately trying to start up). Looking at VCC on an oscilloscope may help check whether it's really a power supply issue.
Can you try powering it from an external voltage source?