Let me try to give you an idea of capacity.
We (wife, 11 yr-old daughter and me) fly our 337G from Miami to a house we have on a Bahamas out-island one hour away. Sometimes for a weekend, more often for several weeks. Because groceries there are limited (not much selection), not as high quality and much more expensive, we tend to take enough food for the stay. On the other hand, we have clothes there and we have a stockpile of non-perishable things like soft drinks. Every single inch of volume inside the plane is
always full. It's like a gipsy van.
I think that you will find a need for the cargo pod, given your family size. The 630nm trip is doable without re-fueling if you have auxiliary tanks and your family can go 4 hrs+ without a real potty break. On my 337G I'd put at least 100 gal for 5 hrs of flight at 150 kts. If it had an RT Aerospace cargo pod of 36 lbs (
www.rtaerospace.com/Cargo_pod.htm for description), I'd still have 1025 lbs for people and luggage, which appears sufficient for your family. But it will be cramped.
Incidentally, if you look at my post in the "Annual Costs" thread, my annuals are a lot less (typically $2,000 and total yearly maintenance at $3,000 to $4,000). You need to find the right mechanic and do some of the work yourself (particularly looking for used parts), but it's a worthwhile goal.