It always sounds like a blown speaker. Welcome to low budget audio recording and playback.
Unless you gut it and replace the custom board with your own MP3 or other higher quality recording- you are not making it any better.
This is the board, and again, this is how they all sound. There is no magic fix. It's NOT the speaker.
I put one of those boards into the operating boxcar for fun.
This was the speaker I used, but tried several, it did not matter the board is what the board is.
"MakerHawk 2pcs Speaker 3 Watt 8 Ohm Single Cavity Mini Speaker Full-Range Cavity Mobile Portable Advertising Machine Speaker Connector Separating Interface" from the A website.
If you want better sound, again, you need a better recording, and then an all new board to play that recording.