USB (360) to PS2 conversion

So I found a used copy of Arcana Heart yesterday at GameStop, and I want to get into Melty Blood when AA comes out next month. Problem is, I don’t have a PS2 stick. I have a TE and a Hori EX2, both for 360, so they connect via USB port. Can I (and how would I?) go about dual-modding so that I can use these on PS2?

Would a PS3 dual mod work?

EDIT: Glanced over the sticky about MC Cthulhu boards. Is that what I want?

Yes, you could do it with a Cthulhu. Just keep in mind that the USB connection won’t work on a PS2, so you’ll need to get a PS2 controller cable and solder it onto the proper connection points on the Cthulhu.

Also, the EX2 is non-common ground so you won’t be able to dual mod that (not easily anyway), but the TE should be fine.