The key here is whether the 4K stick can be set to output at 720p. It’s a resolution used by NowTV devices, and possibly iPlayer, as I recall, but little else. Your best bet, in the absence of any other responses, is to contact Amazon.
It should be able to output 720p OK but depending on the HDMI version the TV uses it may not autodetect it properly - in that case you can manually set the stick to 720p using a higher res. Tv
As in I thought the non 4k type may support down to 1080p and 720p.
I'm also reading elsewhere that the Pioneer may not support HDCP which may cause connection issues with the firestick.
Bought the Roku and all working fine, however HD content does tend to buffer a bit, probably down to it being wireless and and not hardwired connection.