You say it uses standard SMA connectors? Those are the connectors for coaxial cable if I recall right. Google says the maximum run for coaxial cable is 500 meters (~1,600 ft). But that is probably when used for a TV system. I do not know if your little modem (which is designed to have the antennas directly attached) can run over coaxial, let alone the resistance of 500-1000 ft of it.
That brings me to some questions: 500 to 1000 is a large range, could you be more precise? Do you have a budget? What is at the property edge (she, power, ect). How would you get any cable out there, do you have a trench?
There are wifi solutions that could reach out (directionally) over 500 to 1000 feet, but you are talking a over a grand and needing power out there.
They do make LTE signal boosters. I do not know much about they, but a quick google says they are $500 - 1,500. I don't know if they have a better antenna and could be placed in the home of if they would need to be placed on the edge of the property. The added hop for internet may add latency.
You are probably in the range where if you placed the modem at the property edge and converted the network signal to fiber (that's likely too far for ethernet) you could run it to the house and then convert back to ethernet for the short run to your device or devices. It would probably be costly as well.
How was the DSL acting up? And did the company try and fix it?