If I were to do this simply, I would try something rather funny:
1. I would choose the smallest possible shoulder bag that would carry the photo equipment.
2. I would choose a general purpose bag in the dimensions you mentioned.
3. I would put the small shoulder bag inside the bigger one.
4. I would fill the rest of the bag with all necessary items.
It's not funny at all! For overnight trips, I often pack my photo gear into a Lowepro Flipside 300 (which it is essentially a perfect fit for the gear the OP lists), then put that backpack, it change of clothes and a sundries kit into a Storm im2500 carry-on hard case. That way, the gear is protected in the event that it must be checked (hasn't happened domestically with priority boarding, but it might, and standard sized cases don't fit in the regional jet overheads). It also gives me a way to lock up the gear in a hotel room. The case rolls conveniently through the airport, and I have a dedicated photo backpack for outings at my destination.
For longer trips, there's not enough room to store a wardrobe in the carry-on so I'm checking a bag anyway. But I still do the above, so I have at least one change of clothes if the checked bag gets lost.