Does the Lovely Howz of Badges in Paper Mario the Thousand Year door ever remove duplicate badges?

Now I am probably going down a ridiculous path by trying to actually attempt this after all these years, but what I'm trying to do is get 100 copies each of the HP Plus and FP Plus badges found in the Pianta Parlor so that I can then max out my level with nothing but badge point upgrades and then be able to change my health and fp at will at any time in the game.

The problem however is that the Pianta Parlor gets rid of the badge after the beginning of the 7th chapter (the moon world) so one cannot just keep playing the game and eventually get all of the ideal maximum number badges. However, I was thinking that I could buy them and then resell them at the badge shop in Rougeport. I checked and it isn't a large recoup but it's enough to allow me to likely continue farming coins in an efficient manner. I won't have to restart my operations. However, I don't know whether or not the shop actually gets rid of any badges ever. I know it's in theory not supposed to, but I'm wondering if there is a chance that say.... 80 HP and FP badges in their stock might eventually change to 5 in stock thereby preventing me from using them as a money recoup.