Firstly, get Palette Suite by Toxicbunny.

Get the Jazz palette. Don't know where to get it, tough. Ask me to send it to you.

Convert your tileset to 180 colors in PSP, and then save that palette. (don't save the tileset, but undo the 180 colors afterwards)

Take the Jazz palette and paste the palette you just saved into it(using two instances of Palsuite)
Take the transparent color you used out of your old palette, before pasting. Also take out all the pure blacks(0,0,0 RGB).
Change the black at the start of the newly assembled palette into something unused like ugly pink, and save the palette.

Then load it into your tileset(remember to back it up!), and voila, I think. I haven't even covered textured bgs yet, but you know them, I think.

I think I forgot something, I don't know.