If you are not against a little weed killer then you can keep this and other weeds in check. my choice is Killsall. It ha worked the best for me for years. Spray the thistle and puncture weed first wait till They all dies clear them off and plant you huttinea. When it looks like it is getting places you do not want it. Spray it. If you pull it you leave a part of the root and it will just come right back where you don't want it to be. Killsall kills the root thus keeping it in check. IMHO this is what it would do were I you.

I have chameleon plant, lots of it. Mind you, it is pretty when there is a lot of pink. Whenever someone wants some, I make them promise they will plant it in pots.

caw_in_zn5, gravel reminded me of a plant I received as a gift this summer. Its roots were growing in a lump of clay and gravel. I believe it is Sedum oreganum. It is native here in Oregon.