Problem is there are finicky people who will insist that they like the DS3 more than the DS2 and say it feels better. So you’ll end up with no choice but to have to mod the DS3.
As for how expensive it would to make a DS3 work on 360, the only cost in parts is having the DS3 (ranges from $0 to $50), the paewang pcb ($40), and a 20pin ffc connector (um 50cent?) (also a microchip ($2) if you wanted to mod the left analog stick for digital dpad inputs). It will end up costing around the same as the DS2 route.
Sure the mod will be harder than going the converter route, but pays off big time in the fact that you don’t have to worry about carrying a mess of converters. Everything is wrapped up in one lil package.