The Amsoil ASE mentioned is a stout oil and specifically recommended for engines such as yours. Schaeffers 5W-40 syn or 15w40 blend are both very good, and sold by distributors. Contact site sponsors for either of these, perhaps.
"HDEO" or heavy duty engine oil is commercial oil meeting specs for over the road trucks and others, and is low wearing, cleaning running, and long life in diesel or gas engines. Synthetic HDEO could possibly last longer in service and temperature extremes but will cost more up front.
Some grades of HDEO are 15w40, 5W-40 (usually syn), 10w30, SAE 30, and 15W-50.
Some oils that I have used in addition to the others already mentioned:
Rotella 5W-40
Mobil 1 Turbo Diesel Truck 5W-40
Amsoil ACD 10w30/SAE 30
Mobil 1 15W-50
Please don't use regular syn "PCMO" or passenger car motor oil, such as Pennzoil Platinum 10w30. These oils work well for fuel economy in a water-cooled car engine, but too thin and low Zn/Ph for heavy duty use in your ZT's Kaw engine for best protection.
If you really still want to use PCMO syn, then consider something like "GC" or Castrol Syntec 0w30 or M1 High Mileage 10w30 or 10W-40. These are a step up in viscosity and wear protection at operating temps while still keeping the engine clean at higher operating temps of air-cooled engine summer use.