Indeed I tried it and it didn't work. There are HDMI 2.0-to-1.4 converters, but no to-1.1 converters, as it seems. My whole home cinema system including a large CRT projector is about 10 years old, and has no HDMI ports, except for the HDMI 1.1 ports on my AVR. I tried an HDMI-to-SCART converter, which worked but the quality was just too poor on my 95" wide projection screen. Next I'm going to test an HDMI-to-YPbPr component converter to see whether this provides an acceptable solution for the Firestick.
But I really wanted to avoid a digital-to-analog conversion, hence my question.