Have a look at audio pro speakers they should work nicely for you although again no audio delay option.
Bit big tick for sound quality, size and portability.
Try and buy one of the bluetooth speakers then you can try connecting by bluetooth directly to the fire tv stick which from memory i'm sure you can do as i used to do it with the cube although also found sound out of synch depending on what was being watched, the audio pro would also have an aux in depending on model some offer both 3.5mm and rca inputs for connecting to the projector if it offers audio out directly. A number also offer a sub out if you decide you need more low end grunt for movies.
Guessing because you put $ you are in the US - link for US site offering some big discounts at present -
https://us.audiopro.com/shop/
I own a Drumfire, the sub is great but a fairly big unit, you can split the top off so could leave sub with projector and move top part of speaker around house for music and a C5A Addon - has built in Alexa for ease.