I have seen alot of implementations where there is no core layer. Access layer will be a shassis fully ocupied with user ports and everything thing else connects to the core which does distibution functions.
What are you useing at the access layer ?
I see no problem with what you are doing, the cisco heirachial model guides routing at distribution so you could move you sup3s to distribution if you have enough of them? If you are financially constrained, the design you have is fine.