Do you think if I got the omni it would pick it up on skip?
Very little skip is on UHF frequencies though you may be able to get the VHF link on a very excellent and lucky day.
You're going to need more than a very tall tower. I was once flying in a cessna at 6500ft listening to UHF cutting in and out on a XTS2500 from 150 miles away in flat florida. Now this was a rubber duck and not a full wave antenna but the station was just barely receivable from that altitude. You probably wont get squat even on a tower 250 miles away on UHF.
You could buy an AWACS if you have the money though.
Distance to horizon is measured as: D=3.57√h (h being the height in meters) (d being the distance in kilometers)
so at 250 miles (402km) use the calculation 402/3.57=√h or (402/3.57)²=h
So the altitude required is: 12679m or 41597ft
Now this isn't absolute as this does not account for atmospheric refraction. It also does not factor in the height of the transmitter. The actual distance to horizon is going to be farther than this, so the height required is going to be less than what the math tells you, but it's still going to be more than likely out of reach even on a good day. This formula is also intended for light waves and not Radio but the principles are the same.