Dr. Tim,
You may well have a valuable piece of wood for pistol stocks. Dogwood is very dense and difuse porous if I remember correctly, and was used for shuttle blocks in the textile industry and also for golf club heads until recent years. Back in the '60s when I was in industrial forestry I sold tons and tons of Dogwood to a manufacturer of shuttle blocks in the Columbus, Georgia area. The extremely dense non-porous grain wouldn't splinter which made it perfect for spindle blocks used in weaving thread.
If you can split the chunk along the fork and end up with two approximately equal pieces I think you would be OK in doing this. The unique grain characteristics of this wood isn't going to let the end grain split and check to any degree. If it's been cut a month and the end grains aren't splitting by now, it probably won't check very much. Just to be safe you might dip the ends of each piece in melted beeswax or simply paint roofing compound over the ends. I would dry it simply by putting it in the corner of the workshop or garage where air can circulate around it freely. Inside out of the rain, naturally. How long? I don't know, but I would say for at least a year and it might take two. The moisture content in hardwood lumber drops rapidly initially, but then it slows down. The general rule of thumb for air dried hardwoods is about 9-10 months per inch of thickness. Someone may have better ideas about drying it. My limited experience has been with commercial mills with dry kilns, and that doesn't apply here!
One other thing.... The long horn that you asked me about:
If you will email or IM me your address I'll send it up to you for your inspection. I don't have anything in it moneywise, and don't want anything out of it. If you can use it to make an historically correct copy of the large Georgia Horn, then I'll ne pleased for you to use it.
Well, already you have two totally opposite opinions on the ends checking! I'm going to defer to Mitch as he probably has experience with Dogwood and I certainly don't. Is there any evidence of the end grain checking at this point?