Just a thought,
Perhaps contact your local commercial rental equipment store and see if they have a large compressor with air hoses to attach to a thumper-mole/mole for installing conduit pipe for duct banks - whether it's for medium to large diameter galvanized and/or PVC conduit full 10' pipe.
You'll be able to punch a hole straight through the center of the culvert typically without it diverting into the culvert pipe itself. Once it clears the other end, then run whatever pressured water through it to clear the rest of it out and/or pressured air from the commercial air compressor itself.
Good luck 'J', hope you get it worked out.
Below is an example or kind of equipment that I was referring too. Back in the day when I did underground construction electric distribution work professionally, I often used this equipment. Simple to acquire and to operate. Does a fantastic job too without having to dig long and big trenches. They come in a variety of sizes as well.
Piercing Tools
Pneumatic piercing tools are commonly used for the trenchless installation of underground water lines, utility piping, sewer lateral lines, sprinkler lines, electrical lines, telephone lines, cable television lines, sewer conduits and utilities without the need for opening a typical trench or excavation. Piercing tools are routinely used for compaction boring under landscaping, sidewalks, driveways and roadways. NTS carries a complete line of the most commonly used sizes of pneumatic piercing tools for rental and sale. Repair and maintenance of these tools is available at all of our locations.
NTS carries a complete line of pneumatic piercing tools in sizes from 1-3/4” to 7” and all are available for sale or rental. Standard NTS rental packages include the boring tool unit, air tool lubricator and a 50’ air hose which is used between the tool and the lubricator. Piercing tools are reversible for use in areas with limited exit pits. The piercing tool is powered by a standard trailer mounted air compressor that can produce 110 PSI. Typical bore lengths using piercing tools are from 15 to 75 foot long.
Source: https://www.ntsafety.com/product/piercing-tools/