Here are a couple of pieces I have that may work? They are both air dried for many years. Most of what I have in your size requirement have some type of defects.( Knots,bark inclusions,etc.)
A- Is planed to 1" but only 7 1/2" wide by 19" long. ($45 plus shipping)
2- is rough sawn 1 1/16 " thick by 9" wide by 19" long. ($30 plus shipping)
Pictures are of dry wood.
Here is another for your consideration. Rough sawn and air dried. Measures 7 1/8 x 21 x 1 1/8. $35 plus shipping. (The walnut in the bark part of the crotch is pretty cool IMO.)