Nothing wrong with the way you feel. Perhaps your analytical side says a streamer will net you the better sound but your subconscious is telling you an amp will do it. Without getting into the psychology of it. Perhaps your subconscious it right. Amps really impact the sound of your system... of course all the components do... but the steamer is a bit more about detail fine nuance and the amp is about heft among other things. Your speakers are not tremendously efficient... so, it is very possible a great amp would make a huge difference.
It also sounds like you are really wondering what a real audiophile piece of equipment sounds like. When I got my first job out of college I took out my first loan to buy a true state of the art piece of audiophile equipment... a Threshold s500 amp... $5K... $20K in today’s dollars. It was one of a couple revelatory leaps of faith I took that lead me to the great / rewarding journey I have been on to assemble the system I have today.
Maybe consider, making that leap. Don’t rush. Take a trip to a city... spend the weekend, visit several places. Research the heck out of it. Then find some way to finance / pay for a really great amp. Typically I will have an amp for ten to twenty years, before I upgrade, I had a Pass x350 for 17 years and only lost 500 dollars from what I paid for it! Audiophile stuff keeps its value long term.