A six-foot hole is far too deep for a fence company.
You might have to split that job; one to dig the hole and another to set the pipe and concrete.
I'd look at well-drilling companies, including those that bore monitoring wells. I'd also look at contractors who installs bollards like you find at tractor trailer loading docks. A pile-driving company would also be worth looking at.
You might find a capable company that normally does septic systems or landscaping. Landscaping companies often dig out dry wells.
Politicians’ handlers put a high minimum wage in place to incentivize employers to hire illegal aliens under the table.