Unless the top of the tree is dead, I would strongly recommend leaving the tree. If you change your mind later it will take 150 years to grow one back that big.

Depending on the type of tree, you'll end up weither with a live stump that is constantly fighting to grow back or a dead stump that will harbor all sorts of insects and other vermin. Either way doesn't work too well.One the other hand, I have successfully integrated trees into designs to create a more "organic" flow, which works very nicely if you understand some of the limitations of having a living thing be part of your design.

I think it would be fun to break away from the rectangular area and create a series of curved levels, but it would involve a phenomenal amount of earth moving and retaining walls to stabilize the area. Your main area is at the bottom of a slope and you don't want a mudslide every time it rains.

The first thing to do when designing a useful and fun outdoor area is to visualize what you will be doing out there. Who is cooking? Is it more than one person? What kinds of things do you (or would you) like to cook outside? Would you want to have other refreshments? Would you enjoy having a serving counter or bar next to the grilling area? You get the idea . . .

Some practical questions for layout purposes might be: Where does the sun set? Will I be staring at the sun while trying to use the grill? Is the primary griller right or left-handed (you'll want work surface on the opposite side of the grill)?

So many questions to ask . . .

I'd suggest starting an idea book and we'll see if we can't help you fit it into your unusual space.

Terrace the slope and fill with colorful plants. A pea gravel area under the trees would allow for a sitting area. Leaves easily blow off.