Do any rental car companies in the US rent out manual transmission cars?
None of the major ones do, or at least not that I've seen in recent years (and I rent 3-4 times every month).
You might find a "Rent-A-Wreck" type place that does, but still not likely. A car with a manual transmission in the US limits the number of customers they can rent it to, so most places are going to avoid them.
The only "normal" rental I've seen in years with a manual was a base Ranger.
Now? Probably none in the US unless you go with a specialty rental company.
And what incentive does a rental company have to offer a manual?
The savings on the front end is not enough to offset the potential clutch replacement cost liability.
"I owe it to myself, and to my choir students, to not be upset about barns."
You need at least sixteen pigs to finish the job in one sitting, so be wary of any man who keeps a pig farm. They will go through a body that weighs 200 pounds in about eight minutes. That means that a single pig can consume two pounds of uncooked flesh every minute. Hence the expression, "as greedy as a pig.