Glad you found someone to kiln dry your slab. That will set the pitch and sterilize the wood in case there are any eggs or larvae inside that could hatch out and emerge later. A solar kiln will not stay hot enough for long enough to sterilize even 4/4 lumber, much less a slab.
Mine will reach 150 degrees+ in the summer when the sun is high but that optimum time doesn't last long. The lumber needs to reach 132 degree throughout the plank and remain there for at least four hours. I doubt a slab would ever reach that temperature at the core in a solar kiln, much less maintain it for four hours. If the kiln could rotate and track the sun, then it would probably stay hot long enough but that would be an expensive feature.
No harm in sealing the ends of the slab but it's not necessary on Pine. The sap is self-sealing. Sealed or left unsealed, however, there will be some checking on the end grain. That's a good reason to dry the entire slab and then any checking can be cut off. You will also have the entire slab available to select the best looking area for the 7' section you need.
I think that epoxy bar-top finish at Home Depot is ideal for a bar top. It will protect the wood from scratches, etc. but it will also greatly inhibit moisture exchange so the wood won't move much, if any, from seasonal humidity swings.