I also like to eat them right away. We usually have a couple of meals during the first week of season when everyone is still there.
My older brother cleans them up and slices about 3/8" to 1/2" thick. He removes all the junk as stated above.
We have a gas grill at the cabin so I use an A-Maze-N smoke tube to get some flavor. I season them with whatever steak seasoning I enjoy at the time and then I cook them with no flame and the smoke tube (depending on outside temp) for about 45 minutes. Then I light up half the grill to finish them on low. I don't believe I stick a thermometer in them, but the goal is medium rare.
The results are spectacular. Save the tips for the newbies. They will be hooked for life.
If possible, serve with a good red wine in a well used coffee cup. Side dishes are optional. Looks like I had left over venison hamburger beans. Paper plates add a touch of class also.
Now my tummy is rumbling. Thanks a lot!