Are you sure you don't mean thin, right? It can never be too thick
Believe me I feel your pain. Paper is an investment for me too. When I was younger I used the normal A4s (the computer ones) but I painted with pretty dry watercolors, no big washes at all and then I used a warm iron to flatten it (between two blank pieces of paper, so I didn't ruin anything) This piece here [link] I had to photoshop the white background because it was really wrinkled.