I have experience that CX allows me checking-in more than the allowance in terms of number of pieces when my ticket was a piece based ticket. But that time the overall weight of my baggage does not exceed the limit if it is on weight base. Therefore, you may be able to check-in 3 pieces as your 3rd one is really light.

I think the worst case is find some tape to wrap it to your check-in bags and make it one piece, unless your item is a fragile one.