According to Belden, their RG-8x has a maximum pulling tension of 75 pounds. Pulling tension is the amount of force used to pull the cable through a conduit for installation, not long term.
Long term exposure to ultra violet, temperature swings and anything else might change that.
Figuring out the ice loading would take some work, as that would add to the weight.
Then you have to consider how to support it on each end if you were just using the cable without a support messenger.
I think the idea of lashing it to a support messenger is a better idea. I'd use a steel cable to do that, not any sort of rope. Rope will stretch with weight where the coax will not. Putting in a messenger cable to act as you support and then lashing the coax to that would be easy and provide a longer term solution.
If 50Ω isn't a requirement, there are a lot of RG-6 and RG-11 cables out there that have built in messengers designed for supporting the cable from the pole to the house. I don't think I've ever seen a 50Ω cable with one, though.