Pony--absolutely agree--for a party of 10 anywhere on island, reservations are an absolute necessity!
One thing you should check into, is the closing schedule for the restaurants in Grand Case, as many of them close for various periods of time between September and October. So, if you hit on just one particular restaurant, you will need to confirm with them that they will in fact be open on your date. Which of course you can do, when you make your reservation.
I just want to get the scenario straight here--you are coming in, with a party of 10 people. Even if you could find a van to rent, it will be REALLY expensive, and you may have trouble getting one rented for one day. Two smaller cars would be a better choice, in all likelihood. Is everyone on the same flights? If not, it might be better to have more than one vehicle regardless. And are you going to need to provision? If so, again, two vehicles would be a better choice. One vehicle goes to provision and the other takes all the luggage. I believe you may be able to rent a van, but parking a van in Grand Case -- or anywhere else on island -- may be difficult. You could contact Wilfred Brooks, who is a TTOL sponsor--click on his link on the sponsors page. He has a large van that could possibly pick you up at the airport, but I think even his van is probably not going to hold 10 people AND luggage. You could perhaps have him take most of the people and the luggage to your hotel, and have the others rent another car to provision in, if you need to provision.
If it were ME, and I positively wanted to stay on Orient Beach, I would probably plan on dinner in Orient Village, as compared to going to Grand Case. There are many great restaurants in Orient Village. And frankly, you are talking the day of arrival for this big meal? I have to say that I personally am too tired and grumpy to enjoy a really upscale meal that first night and the cost is somewhat of a waste. Orient Village has some different types of restaurants, casual and also more upscale, for those who might have different ideas for their meal. For hotels on Orient, I would check out La Playa, Orient Beach Hotel or Esmerelda. From La Playa and Orient Beach Hotel, you could walk to several different restaurants in Orient Village. Renting this far in advance, you could possibly rent a whole building at Esmerelda. The buildings are about 4 units per building. The units there surround a pool, so you'd have that pool to your group, as a private pool. Esmerelda has a very excellent restaurant right there on the premises, or you could head down to the Village for dinner, but probably you would need transportation, as it's a bit of a walk from there to the Village.
OR, as someone else suggested, stay at GCBC, L'Esplanade or L'Petit. Again, GCBC has an excellent restaurant right there on the premises.
I just think you need to evaluate for sure whether your plan will work, after a long travel day.
Best wishes with your planning!