Two tickets for the same day
 

So my wife and I each had 2 e-credits certificates for Delta. They were unable to combine the credits because they were restricted credits for being bumped off flights.

We instead just booked two separate tickets each to get to Wyoming.
So we have a flight from ROC-JFK on one confirmation number then JFK-SLC-GCC on another ticket. We are planning on having checked bags since its a week long trip.

Also it was cheaper by like $10 to do it this way. But really it was so we can use vouchers instead of paying cash.

Is there a way to not have to go to baggage claim at JFK to grab our bags just to check it back in?

I don't understand your situation with the credits...(why not just apply the credit to the overall ROC-GCC trip?) but I will add my two cents on the bags.

What you can do, is ask the agent (not a skycap) at ROC to check your bag all the way through to GCC and it will automatically be transferred in JFK and SLC. They will likely ask for proof of that onward itinerary, so be ready to show it. Since you're on DL the whole way, it should be pretty easy.

We had two credits one for $300+ another for $600. The trip from ROC-GCC would cost $780+. They could not combine the two credits to cover the trip so we decided to split it. ROC-JFK for 170 and JFK-GCC for 607.