So while looking up these hunts I also came across the following Goat/Capra hunts and have listed them in comparison as these species are often hunted in the same terrain as the sheep and often included in a combination hunt with the above.
DIY Tahr & Chamois hunt in New Zealand, just the cost of the licenses and travel.
Mountain goat hunt in
British Columbia, $9,500 (booking this one).
Mountain goat hunt in
Alaska, $18,500.
Rhonda Ibex hunt in
Spain, $3,900.
Ibex Grand Slam (4 Species) in
Spain, $21,000.
Mid-Asian Ibex hunt in
Kyrgyzstan, $7,500
Bezoar Ibex hunt in
Turkey, $10,000
Dagestan Tur hunt in
Russian, $6000.
Markhor hunt in
Pakistan, $128,000.
As you can see, aside from the Markhor, the Goat/Capra hunts present an affordable alternative if sheep are above your budget.