I appreciate wanting to go the DIY approach, and it looks to me like it would technically work as far as the pieces going together.

Would I recommend it though? Probably not. The LED strips are generally not great for lighting up a whole band like that. It can be done for sure, but I'd be skeptical about making it look good.

Honestly it would be cheaper just to get off-brand par cans like these ones and control them with the DMX controller you linked. Keep in mind in either case you will need to buy DMX cables as well and likely cable extensions for the LED strips if you decide to go that route.